Publications of Yuan Xu

Books

• "Minimal Cubature Rules: Theory and Practice", Cambridge Monographs on Applied and Computational Mathematics 45, Cambridge Univ. Press, 2025. ISBN: 9781009663922.
• (with Charles F. Dunkl) "Orthogonal Polynomials of Several Variables", Second Edition, Encyclopedia of Mathematics and its Applications, vol. 155, Cambridge Univ. Press, 2014. ISBN: 9781107071896.
• (with Feng Dai) "Approximation Theory and Harmonics Analysis on Spheres and Balls", Springer Monographs in Mathematics, Springer, 2013. ISBN: 978-1-4614-6659-8 (Print) 978-1-4614-6660-4 (Online). Errata
• (with Charles F. Dunkl) "Orthogonal Polynomials of Several Variables", Encyclopedia of Mathematics and its Applications, vol. 81, Cambridge Univ. Press, ISBN 0-521-80043-9, 2001. Errata
• "Common Zeros of Polynomials in Several Variables and Higher Dimensional Quadrature", Pitman Research Notes in Mathematics Series, Longman, Essex, 1994.
• Translation from English to Chinese: "Men of Mathematics" by E.T. Bell, Shang Wu Pub. House, Beijing, 1991, 2nd printing, 1995. Reissued by Shanghai Scientific and Technological Education Pub. House, 2005, 2012.

Lecture notes

• (with Feng Dai) Analysis on h-harmonics and Dunkl Transforms, Advanced Courses in Mathematics - CRM Barcelona, Birkhauser, 2015. ISBN 978-3-0348-0887-3.
• Lecture notes on orthogonal polynomials of several variables, Summer School on Orthogonal Polynomials, Harmonic Analysis, Approximation and Applications, Inzell, Germany, Sept. 2001. In "Advances in the Theory of Special Functions and Orthogonal Polynomials," p. 141-196. W. zu Castell, F. Filbir, B. Forster (eds.), Nova Science Publishers, 2005. Inzell.pdf

Book chapter

• Orthogonal polynomials of several variables. Chapter 2 of Encyclopedia of Special Functions: The Askey-Bateman Project. Volume 2. Multivariable Special Functions, Cambridge Univ. Press, 2021, pp 19-78. AB-Chapt2

Edited In Memoriam

• In Memoriam of Donald Newman (1930 - 2007). J. Approx. Theory, 154 (2008), 37-58. Newman
• In Memoriam of Borislav D. Bojanov (1944 - 2009). J. Approx. Theory, 162 (2010), 1739-1765. (co-edited with A. Kroo and A. Pinkus) Bojanov
• In Memoriam of Hubert A. Berens (1936 - 2015). J. Approx. Theory, 198 (2015), iv-xxix. Berens
• In Memoriam of Ward Cheney (1929 - 2016). J. Approx. Theory, 213 (2017), iv-xxxii. (co-edited with Dany Leviatan) Cheney

Papers

Submitted

• Approximation and orthogonality on fully symmetric domains. FullySymmtric
• (with Y. Ge) Best approximation by polynomials on conic domains. Approx_cone
• (with M. Dressler, S. Foucart, M. Joldes, E. de Klerk, and J. Lasserre) Least multivariate Chebyshev polynomials on diagonally determined domains. LeastPoly2
• (with T. Sauer) Continued fractions and orthogonal polynomials in several variables. CF_OP

Accepted

• Minimal cubature rules and Koornwinder polynomials. Indag Math. minimal_CF

2025

• (with J-B. Lasserre) A Generalized Pell's equation for a class of multivariate orthogonal polynomials. Trans. Amer. Math. Soc. 378 (2025), 5305-5328. SumSquare
• (with Y. Ge) Sharp Bernstein inequalities on simplex. Constuctive Approx. 62 (2025), 305-328. B-ineq
• (with N. Proudfoot, B. Young) On the enumeration of series-parallel matroids. Adv. Appl. Anal. 163 (2025), Part B, 102801, 13 pp. braid_matroid
• (with M. Dressler, S. Foucart, M. Joldes, E. de Klerk, and J. Lasserre) Optimization-aided construction of multivariate Chebyshev polynomials. J. Approx. Theory 305 (2025), 106116, 19 pp. LeastPoly1
• (with M. Buhmann) Positive definite functions on a regular domain. IMA J. Numer. Anal. 45 (2025), 2824-2843. PDFunction

2024

• Orthogonal polynomials on domains of revolution. Studies in Applied Math. 153 (2024), Issue 2, e12703, 38 pp. Rotation
• Highly localized kernels on space of homogeneous type. Constructive Theory of Functions , Proceedings of the International Conference Lozenets, June 11-15, 2023, Bulgarian Acad. Sciences. Lozenets
• (with M. Buhmann and J. Jager) l^1-summability and Fourier series of B-splines with respect to their knots. Math. Z. 306 (2024), Paper no. 53, 16 pp Bspline

2023

• (with M. Fasondini, S. Olver) Orthogonal polynomials on a class of planar algebraic curves. Studies in Applied Math. 151 (2023), 369-405. OP_curve
• Bernstein inequality on conic domains and triangle. J. Approx. Theory 290 (2023), Paper no. 105889, 30 pp. Bernstein
• Approximation and localized polynomial frame on double hyperbolic and conic domains. Constructive Approx. 57 (2003), 921-976. ConicDomainsII
• (with R. Aktas, A. Branquinho, A. Foulquie-Moreno) Monomial and Rodrigues orthogonal polynomials on the cone. J. Math.Anal. Appl. 522 (2023), no. 2, Paper no. 126977. 26 pp. MOPcone
• Fourier orthogonal series on a paraboloid. J. d'Analyse Math. 149 (2023), 251-279. Paraboloid
• (with M. Fasondini, S. Olver) Orthogonal structure on a cubic planar curve. Found. Comput. Math. 23 (2023), no. 1, 1-31. OP-cubic

2022

• Maximal functions and multiplier theorem for Fourier orthogonal series. J. Functional Anal. 283 (2022), Paper no. 109648, 33 pp. MaximalFunc
• (with P. Iliev) Hahn polynomials for hypergeometric distribution. Adv. Applied Math. 139 (2022), Paper No. 102364, 34 pp. HD-Hahn

2021

• Approximation and localized polynomial frame on conic domains. J. Functional Anal. 281 (2021), no. 12, Paper no. 109257, 94 pp. ConicDomains
• Laguerre expansions on conic domains. J. Fourier Anal. Appl. 27 (2021), no.4, paper no. 64, 36 pp. Laguerre
• Intertwining operator associated to symmetric groups and summability on the unit sphere. J. Approx. Theory 272 (2021), 105649, 16 pp. V-symmetry
• (with S. Olver) Non-homogeneous wave equation on a cone. Integral Transforms Spec Funct. 32 (2001), 604-619. wave-eqn
• Orthogonal structure and orthogonal series in and on a double cone or a hyperboloid. Trans. Amer. Math. Soc. 374 (2021), 3603-3657. hyperboloid
• (with S. Olver) Orthogonal structure on a quadratic curve. IMA J. Numer. Anal. 41 (2021), 206-246. OP-quadratic

2020

• Intertwining operators associated to dihedral groups. Constr. Approx. 52 (2020), 395-422. V-Dihedral
• (with S. Olver) Orthogonal polynomials in and on a quadratic surface of revolution Math. Comp. 89 (2020), 2847-2865. OP-surface
• Orthogonal polynomials and Fourier orthogonal series on a cone. J. Fourier Anal. Appl. 26 (2020), Paper No. 36, 42 pp. ConeOP
• (with P. Iliev) Hahn polynomials on polyhedra and quantum integrability. Adv. Math. 364 (2020), 107032, pp 37. Hahn-polyhedra
• (with G. Kerkyacharian and P. Petrushev) Gaussian bounds for the heat kernels on the ball and simplex: classical approach. Studia Math. 250 (2020), 235-252. HeatKernel2
• (with G. Kerkyacharian and P. Petrushev) Gaussian bounds for the weighted heat kernels on the interval, ball and simplex. Constr. Approx. 51 (2020), 73-122. HeatKernel

2019

• (with D. Dimitrov) Wronskians of Fourier and Laplace transforms. Trans. Amer. Math. Soc. 372 (2019), 4107-4125. WFLT
• (with S. Olver) Orthogonal structure on a wedge and on the boundary of a square. Found. Comp. Math. (FoCM) 19 (2019), 561-589. OP-wedge
• (with H. Feng and C. Krattenthaler) Best polynomial approximation on the triangle. J. Approx. Theory 241 (2019), 63-78. BestAppTriangle

2018

• Approximation by polynomials in Sobolev spaces with Jacobi weight. J. Fourier Anal. Appl. 24 (2018) 1438-1459. 1D-Approx
• (with M. Pinar) Best polynomial approximation on the unit ball. IMA J. Numer. Anal. 38 (2018), 1209-1228, BestAppBall
• Optimal points for cubature rules and polynomial interpolation on the square. Contemporary Computational Mathematics - a celebration of the 80th birthday of Ian Sloan, p. 1287-1305, Springer, Cham, 2018. Cuba-square
• (with N. Proudfoot and B. Young) The Z-polynomial of a matroid. Electon. J. Combin. 25 (2018) no. 1, Paper 1.26. Z-polynomials
• Positive definite functions on the unit sphere and integrals of Jacobi polynomials. Proc. Amer. Math. Soc. 146 (2018), 2039-2048. PDF-Jacobi

2017

• Approximation and orthogonality in Sobolev spaces on a triangle. Constr. Approx. 46 (2017), 349-434. ApproxTriangle
• (with P. Iliev) Connection coefficients of classical orthogonal polynomials of several variables. Adv. Math. 310 (2017), 290-306. ConnCoeff
• Minimal Cubature rules and polynomial interpolation in two variables II. J. Approx. Theory 214 (2017), 49-68. Cuba2d2

2016

• Positivity and Fourier integral on hexagonal domain. J. Approx. Theory 207 (2016), 193-206. PosFourier
• (with D. Dimitrov) Slater determinants of orthogonal polynomials. J. Math. Anal. Appl. 435 (2016), 1552-1572. DetOP
• Orthogonal expansions for generalized Gegenbauer weight function on the unit ball. Contemp. Math., Vol. 661, 2016, 153-165. GGball

2015

• An intergral identity with applications in orthogonal polynomials. Proc. Amer. Math. Soc. 143 (2015), 5253-5263. ReprodKernel
• Generalized characteristic polynomials and Gaussian cubature rules. SIAM. J. Matrix Anal. 36 (2015), 1129-1142. OPzero
• (with F. Marcellan) On Sobolev orthogonal polynomials. Expos. Math. 33 (2015), 308-352. SOP
• Hahn, Jacobi, and Krawtchouck polynomials of several variables. J. Approx. Theory 195 (2015), 19-42. HJK
• (with L. Fernandez, F. Marcellan, T. Perez, M. Pinar) Sobolev orthogonal polynomials on product domains. J. Comp. Appl. Math. 284 (2015), 202-215. ProdSOP
• Uncertainty principles for weighted spheres, balls and simplexes. J. Approx. Theory 192 (2015), 193-214. WeightedUncert
• Complex versus real orthogonal polynomials of two variables. Integral Trans. & Special Funct. 26 (2015) 134-151. ComplexOP

2014

• (with H. Li) Spectral approximation on the unit ball. SIAM J. Numer. Anal. 52 (2014), 2647-2675. SpectralApprox
• Best polynomial approximation on unit sphere and unit ball. In Approximation Theory XIV: San Antonio 2013 , Springer Proceedings in Mathematics, Springer, p. 357-375. SanAntonio
• (with F. Dai) Hardy-Rellich inequality and uncertainty principle on the unit sphere. Constr. Approx. 40 (2014), 141-171. Uncertainty
• (with R.K. Beatson, W. zu Castell) A Polya criterion for (strict) positive definiteness on the sphere. IMA J. Numer. Anal. 34 (2014), 550-568. pdf-sphere
• Tight frame with Hahn and Krawtchouk polynomials of several variables. SIGMA 10 (2014), 019. TightFrame
• (with M. Sawa) On positive cubature rules on the simplex and isometric embeddings. Math. Comp. 83 (2014), 1251-1277. CubaSimplex

2013

• (with R. Aktas) Sobolev orthogonal polynomials on a simplex. Int. Math. Res. Notice, , 2013 (2013), no. 13, 3087-3131. SOPsimplex
• (with T. E. Perez, M. A. Pinar) Weighted Sobolev orthogonal polynomials on the unit ball, J. Approx. Theory 171 (2013), 84-104. SOPball
• Minimal cubature rules on an unbounded domain. Dolomite Res. Notes on Approximation 6 (2013), 3-8. UnbddDomain
• (with B. Rider and C. D. Sinclair) A solvable mixed charge ensemble on the line: global results. Prob. Theory & Related Fields. 155 (2013), 127-164. Two-charge

  2012

• Orthogonal polynomials and expansions for a family of weight functions in two variables. Constr. Approx. 36 (2012), 161-190. OP2d
• (with H. Li and J. Sun) Discrete Fourier analysis and Chebyshev polynomials with G_2 group. SIGMA 8 (2012), 067, 29 pages. G2
• (with K. Ivanov and P. Petrushev) Decomposition of spaces of distributions induced by tensor product bases. J. Funct. Anal. 263 (2012), 1147 - 1197. Poduct Bases
• Minimal Cubature rules and polynomial interpolation in two variables. J. Approx. Theory 164 (2012), 6 - 30. Cuba2d

2011

• (with H. De Bie) On the Clifford-Fourier transform. Int. Math. Res. Notice, (2011), Vol. 2011, No. 22, 5123 - 5163. CliffordFourier
• (with F. Dai) Polynomial approximation in Sobolev spaces on the unit sphere and the unit ball. J. Approx. Theory 163 (2011), 1400-1418. Sobolev
• On Gauss-Lobatto integration on the triangle. SIAM J. Numer. Anal. 49 (2011), 541-548. Lobatto

2010

• (with F. Dai) Moduli of smoothness and approximation on the unit sphere and the unit ball. Advances in Math. 224 (2010), 1233- 1310. Moduli
• Fourier series and approximation on hexagonal and triangular domains. Constr. Approx. 31 (2010), 115-138. AppHexagon
• (with H. Li and J. Sun) Discrete Fourier analysis with lattices on planar domains. Numer. Algorithm 55 (2010), 279-300. PlanarDFT
• (with A. M. Delgado, L. Fernandez, T. E. Perez, M. A. Pinar) Orthogonal polynomials in several variables for measures with mass points. Numer. Algorithm 55 (2010), 245 - 264. OP_MassPt
• (with H. Li) Discrete Fourier analysis on fundamental domain of A_d lattice and on simplex in d-variables. J. Fourier Anal. Appl. 16 (2010), 383 - 433. Ad Lattice
• (with K. Ivanov and P. Petrushev) Sub-exponentially localized kernels and frames induced by orthogonal expansions. Math. Z. 264 (2010), 361 - 397. Sub-exp
• (with L. Fernandez, T. Perez, M. Pinar) Krall--type orthogonal polynomials in several variables. J. Comp. Appl. Math. 233 (2010), 1519-1524. KrallType

SPIE Proceedings

• (with O. Tischenko, A. Schengere and C. Heoschen) Properties of a parameterization of radon projection by the reconstruction on circular disc Proc. SPIE, Vol. 7622, Medical Imaging 2010: Physics of Medical Imaging, 7622F.

2009

• (with Feng Dai) Boundedness of projection operators and Cesaro means in weighted L^p space on the unit sphere, Trans. Amer. Math. Soc. 361 (2009), 3189 -3221. DaiXu3
• (with O. Tischenko) OPED reconstruction algorithm for limited angle problem. J. Inverse Ill-Posed Problems. 17 (2009), 795 - 813. Limited Angle
• (with F. Filbir and W. zu Castell) Cesaro means of Jacobi expansions on the parabolic biangle. J. Approx. Theory 159 (2009) 167-179. Biangle
• (with M. Pinar) Orthogonal polynomials and partial differential equations on the unit ball. Proc. Amer. Math. Soc. 137 (2009), 2979 - 2987. OP-PDE
• (with A. M. Delgado, J. S. Geronimo, P. Iliev) On a two variable class of Bernstein-Szego measures, Constr. Approx. 30 (2009), 71- 91. B-S
• (with H. Li) Discrete Fourier Analysis on a dodecahedron and a tetrahedron, Math. Comp. 78 (2009), 999-1029. Dodeca
• (with G. Kerkyacharian, P. Petrushev, and D. Picard) Decomposition of Triebel-Lizorkin and Besov spaces in the context of Laguerre expansions. J. Functional Anal. 256 (2009), 1137-1188. Lagurerre
• (with H. Li and J. Sun) Cubature formula and interpolation on the cubic domain. Numer. Math. Theory Methods Appl. 2 (2009), 119-152. Cubic
• (with S. De Marchi and M. Vianello) New cubature formulae and hyperinterpolation in three variables. BIT Numer. Math. 49 (2009), 55-73. 3d-cubature
• (with Feng Dai) Cesaro means of orthogonal expansions in several variables, Constr. Approx. 29 (2009), 129-155. DaiXu2

SPIE Proceedings

• (with O. Tischenko and C. Heoschen) Fast implementation of the image r econstruction algorithm OPED, Proc. SPIE, Vol. 7258, Medical Imaging 2009: Physics of Medical Imaging, 72585F.
• (with H. de las Heras, O. Tischenko, H. Schlattl and C. Heoschen) Dose reduction potential of the scanning geometry CT DOR: a simulation study, Proc. SPIE, Vol. 7258, Medical Imaging 2009: Physics of Medical Imagine, 72585R.
• (with O. Tischenko, T. Goetzfried, L. Bogner and C. Hoeschen), Reduction of aliasing artifacts in tomographic images Proc. SPIE 7258, Medical Imaging 2009: Physics of Medical Imaging, 72583F.

2008

• (with G. Kyriazis and P. Petrushev) Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball, Proc. London Math. Soc. 97 (2008), 477-513. KPX2
• (with B. Kroetz and S. Thangavelu) Heat transform for nilmanifolds associated to the Heisenberg group, Revista Mat. Iberoamericana, 24 (2008) 243-266. KTX2
• Sobolev orthogonal polynomials defined via gradient on the unit ball, J. Approx. Theory. 152 (2008), 52-65. SobolevOP_II
• (with P. Petrushev) Decomposition of spaces of distributions induced by Hermite expansions, J. Fourier. Anal. Appl. 14 (2008), 372-414. Hermite
• (with H. Li and J. Sun) Discrete Fourier analysis, cubature and interpolation on a hexagon and a triangle, SIAM J. Numer. Anal. 46 (2008), 1653-1681. LSX
• (with G. Kyriazis and P. Petrushev) Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces, Studia Math. 186 (2008), 161-202. Jacobi_II
• (with H. de las Heras, O. Tischenko and C. Heoschen) Comparison of the interpolation functions to improve a rebinning-free CT-reconstruction algorithm, Z. Med. Physik 18 (2008), 7-16. Z-MP
• (with P. Petrushev) Localized polynomial kernels and frames on the ball, Constr. Approx. 27 (2008) 121-148. PX2

SPIE Proceedings

• (with H. de las Heras, O. Tischenko, B. Renger and C. Heoschen) Experimental proof of an idea for a CT-scanner with dose reduction potential, Proc. SPIE, Vol. 6913, Medical Imaging 2007: Physics of Medical Imaging, 691306.

2007

• (with F. Dai) Maximal function and multiplier theorem for weighted space on the unit sphere, J. Func. Analysis 249 (2007), 477--504. MaximalFunc
• (with L. Bos, S. De Marchi and M. Vianello) Bivariate Lagrange interpolation at Padua points: the ideal theory approach, Numer. Math., 108 (2007), 43-57. Paduva2
• (with O. Tischenko) Fast OPED algorithm for reconstruction of images from Radon data, East. J. Approx. 12 (2007), 427-444. FastOPED
• Reconstruction from Radon projections and orthogonal expansion on a ball, J. Physics A: Math. and Theor., 40 (2007) 7239-7253. Radon2
• (with O. Tischenko, C. Hoeschen) Image reconstruction by OPED algorithm with averaging, Numer. Algo. 45 (2007), 179-193. OPEDave
• (with P. Iliev) Discrete orthogonal polynomials and difference equations of several variables, Adv. in Math., 212 (2007) 1-36. Difference
• (with O. Tischenko and C. Heoschen) Approximation and reconstruction from attenuated Radon projections, SIAM J. Numer. Anal., 45 (2007), 108-132. Attenuated
• (with W. Castell and F. Lain Fernandez) Polynomial interpolation on the unit sphere II, Adv. in Comp. Math. 26 (2007), 155-171. Interpolation II
• (with S. Thangavelu) Riesz transform and singular integrals for Dunkl transform, J. Comp. Appl. Math. 199 (2007), 181-195. Riesz

SPIE Proceedings

• (O. Tischenko, Y. Xu, C. Hoeschen) Improvement of OPED Algorithm by means of introducing an integration in the evaluation process, Proc. SPIE, Vol. 6142, Medical Imaging 2007: Physics of Medical Imaging, 6142-5L.
• (H. de las Heras, O. Tischenko, W. Panzera, Y. Xu and C. Heoschen) Modelling and testing of a non-standard scanning device with dose reduction potential, Proc. SPIE, Vol. 6142, Medical Imaging 2007: Physics of Medical Imaging, 6142-3R.

2006

• Analysis on the unit ball and on the simplex, Elec. Trans. Numer. Anal. 25 (2006), 284-301. Atlanta
• (with L. Bos, M. Caliari, S. De Marchi and M. Vianello) Bivariate Lagrange interpolation at Padua points: the generating curve approach, J. Approx. Theory, 143 (2006) 15-25. Padua1
• A new approach to the reconstruction of images from Radon projections, Adv. in Applied Math. 36 (2006), 388-420. Radon
• A family of Sobolev orthogonal polynomials on the unit ball, J. Approx. Theory 138 (2006), 232-241. Sobolev

SPIE Proceedings

• (with O. Tischenko and C. Heoschen) A new reconstruction algorithm for Radon data, Proc. SPIE, Vol. 6142, Medical Imaging 2006: Physics of Medical Imaging, p. 791-798.
• (with O. Tischenko and C. Heoschen) A new scanning device in CT with dose reduction potential, Proc. SPIE, Vol. 6142, Medical Imaging 2006: Physics of Medical Imaging, p. 893-899.

2005

• (with S. Thangavelu) Generalized translation and convolution operator for Dunkl transform, J. d'Analyse Mathematique 97 (2005) 25-56. Dunkl transform
• ( with B. Bojanov) Reconstruction of a polynomial from its Radon projections, SIAM J. Math. Anal. 37 (2005), 238-250. Radon
• ( with P. Petrushev) Localized polynomial frames on the interval with Jacobi weights, J. Fourier Anal. Appl. 11 (2005), 557 - 575. Jacobi
• Second order difference equations and discrete orthogonal polynomials of two variables, Int. Math. Res. Notice , 2005:8 (2005) 449-475. Difference
• Rodrigues type formula for orthogonal polynomials on the unit ball, Proc. Amer. Math. Soc. 133 (2005), 1965-1976. Rodrig.pdf
• Almost everywhere convergence of orthogonal expansions of several variables, Const. Approx., 22 (2005), 67 - 93. Almost
• ( with B. Kroetz and S. Thangavelu) The heat kernel transform for the Heisenberg group, J. Funct. Anal. 225 (2005), 301-336. Heisenberg
• Best approximation of monomials in several variables, Rend. del Cir. Matema. di Palermo (Proceedings of 5th International Conference on Functional Analysis and Approximation Theory, Acquafredda di Maratea, Italy, June 16-23, 2004), Serie II, 76 (2005), 129 - 155. FAAT04.pdf
• ( with P. Vertesi) Mean convergence of orthogonal Fourier series and interpolating polynomials, Acta. Math. Hunga. 7 (2005), no. 1-2, 119--147. VertesiXu
• Generalized translation operator and approximation in several variables, J. Comp. Appl. Math. (Proceedings of Seventh International Symposium on Orthogonal Polynomials, Special Functions and Applications, Copenhagen, Denmark, August 18 - 22, 2003), 178 (2005), p. 489-512. Transl JCAM.pdf
• Monomial orthogonal polynomials of several variables, J. Approx. Theory, 133 (2005), 1-37. Preprint, May, 2002. Monomial.pdf
• Weighted approximation of functions on the unit sphere, Const. Approx., 21 (2005), 1-28. Preprint, July 2002. Bestapp

2004

• On Discrete orthogonal polynomials of several variables, Adv. in Applied Math., 33 (2004), 615-632. Discrete
• On polynomials of least deviation from zero in several variables, J. Experimental Math. 13 (2004), 103-112. Least, revised Least.pdf
• Approximation by means of h-harmonics polynomials on the unit sphere, Adv. in Comp. Math., 20 (2004), 247-260. ApproxSph.ps.gz
• On polynomial interpolation on the unit ball, Approximation Theory: A volume dedicated to Borislav Bojanov , (D. K. Dimitrov, G. Nikolov, and R. Uluchev, eds.), Marin Drinov Acad. Publ. House, Sofia, 2004, p. 325-337. ball-inter.pdf
• Polynomial interpolation on the unit sphere and on the unit ball, Adv. in Comp. Math., 20 (2004), p. 247-260. ACMinterp.ps.gz

2003

• Polynomial interpolation on the unit sphere, SIAM J. Numer. Anal., 41 (2003), p. 751-766. InterSph.ps.gz
• (with Zhongkai Li) Summability of orthogonal expansions of several variables, J. Approx. Theory, 122 (2003), 267-333. Li-Xu.ps.gz
• Lower bound for the number of nodes of cubature formulae on the unit ball, J. Complexity, 19 (2003), 392-402. CFbound.ps.gz
• Orthogonal expansions and weighted approximation on the unit sphere, Constructive Function Theory, DARBA, Sofia, 2003, p. 156-177. Varna.ps.gz
• (with B. Bojanov) Polynomial interpolation of two variables based on a factorization method. J. Approx. Theory, 120 (2003), 267-282. BoXu2.ps.gz

2002

• An integral formula for generalized Gegenbauer polynomials and Jacobi polynomials, Adv. in Applied Math., 29 (2002), 328 -343. Jacobi.ps.gz
• Biorthogonal polynomials and total positive functions, J. Phys. A: Math. Gen., 35 No. 26 (2002), 5499-5510. Biortho.ps.gz
• (with B. Bojanov) On a Hermite interpolation by polynomials of two variables, SIAM. J. Numer. Anal., 39 (2002), 1780-1793. BoXu1.ps.gz

2001

• Representation of reproducing kernels and the Lebesgue constants on the ball, J. Approx. Theory, 112 (2001), 295-310. Reprod.ps.gz
• Orthogonal polynomials and summability on spheres and on balls, Math. Proc. Cambridge Phil. Soc., 31 (2001), 139-155. Ball-Sph
• (with Hubert Berens, Zhongkai Li) On l-1 Riesz summability of the inverse Fourier integral, Indag. Math., 12 (2001), 41-53. BLX.ps.gz
• Orthogonal polynomials on the ball and on the simplex for weight functions with reflection symmetries, Const. Approx., 17 (2001), 383-412. Classical.ps.gz
• (wiht S. Heo) Constructing cubature formulae for sphere and triangle, Math. Comp., 70 (2001), 269-279. HeoXu2.pdf. Also see LongVersion.pdf, the reference [6] in the paper, a longer version that contains numerical values of the weights and abscissas of the rules.
• Orthogonal polynomials and cubature formulae on the balls, simplices, and spheres, J. Comp. Appl. Math., 127 (2001), 349-368. OP-CF.ps.gz

2000

• (with S. Heo) Invariant cubature formulae for spheres and balls by combinatorial methods, SIAM J. Numer. Anal., 38 (2000), 626-638. HeoXu.pdf
• A note on summability of Laguerre expansions, Proc. Amer. Math. Soc., 128 (2000), 3571--3578. Laguerre.ps.gz
• A product formula for Jacobi polynomials, in Special Functions, Proceedings of International Workshop, Hong Kong, June 21-25, 1999, World Sci. Publ., 2000, p. 423-430. Intertw.ps.gz
• Harmonic polynomials associated with reflection groups, Can. Math. Bulletin, 43 (2000), 496--507. Harmon.ps.gz
• Funk-Hecke formulae for orthogonal polynomials on sphere and on balls, Bull. London Math. Soc., 32 (2000), 447-457. FunkHecke.ps.gz
• (with Zhongkai Li) Summability of the product Jacobi series, J. Approx. Theory, 104 (2000), 287-301. LiXu.ps.gz
• Polynomial interpolation in several variables, cubature formulae, and ideals, Advances in Comp. Math., 12 (2000), 363-376. Interpo.ps.gz
• Constructing cubature formulae by the method of reproducing kernel, Numer. Math., 85 (2000), 155-173. ReprodCF.ps.gz

1999

• Cubature formula and polynomial ideals, Advances in Applied Math., 23 (1999), 211-233.
• (with S. Heo) Constructing cubature formulae for spheres and balls, J. Comp. Appl. Math. 112 (1999), 95-119.
• Aymptotics of the Christoffel functions on a simplex in R^d, J. Approx. Theory, 99 (1999), 122-133.
• (with S. Heo) Constructing symmetric cubature formulae on a triangle, Advances in Computational Mathematics, eds. Z. Chen et al., Marcel Dekker, Inc., New York, 1999, 203-221.
• Summability of Fourier orthogonal series for Jacobi weight on a ball in R^d, Trans. Amer. Math. Soc., 351 (1999), pp. 2439-2458. Preprint, Aug. 1995

1998

• Summability of Fourier orthogonal series for Jacobi weight functions on the simplex in R^d, Proc. Amer. Math. Soc., 126 (1998), 3027-3036.
• Orthogonal polynomials and cubature formulae on spheres and on simplices, Methods Anal. and Appl., 5 (1998), p. 169-184.
Simplex.pdf
• Minimal Cubature formulae for a family of radial weight functions, Advances in Comp. Math., 8 (1998), 367-380.
• Intertwining operator and h-harmonics associated with reflection group, Canadian J. Math., 50 (1998), 193-209.
• Orthogonal polynomials and cubature formulae on spheres and on balls, SIAM J. Math. Anal., 29 (1998), 779-793.
SIAMsphere.pdf

1997

• Integration of the intertwining operator for h-harmonic polynomials associated to reflection groups, Proc. Amer. Math. Soc., 125 (1997), 2963-297.
• (with H. Berens, M. Finzel, W. Li) Hoffman's error bounds and uniform Lipschitz continuity of Best l_p-approximations, J. Math. Anal. Appl. , 213 (1997), 183-201.
• Orthogonal polynomials for a family of product weight functions on the spheres, Canadian J. Math., 49 (1997), 175-192. Sphere.ps.gz
• (with H. Berens) l-1 summability for multivariate Fourier integrals and positivity, Math. Proc. Cambridge Phil. Soc. 122 (1997), 149--172.
• Summability of certain ultraspherical orthogonal sereis in several variables, in The heritage of P. L. Chebyshev: a Festschrift in honor of the 70th birthday of T. J. Rivlin. Ann. Numer. Math. 4 (1997), 623-638.
• On orthogonal polynomials in several variables, Special Functions, q-sereis and Related Topics, The Fields Institute for Research in Mathematical Sciences, Communications Series, Volume 14, 1997, p. 247-270 fields.pdf
• On commuting family of block Jacobi matrices, Comput. Math. Appl. 33 (1997), 211-222.

1996

• Asymptotics for orthogonal polynomials and Christoffel functions on a ball, Methods and Appl. Analysis, 3 (1996), 257-272.
• (with T. Sauer) Regular points for Lagrange interpolation on the unit disk, Numer. Algorithm, 12 (1996), p. 287-296.
• Lagrange interpolation on Chebyshev points of two variables, J. Approx. Theory, 87 (1996), p. 220-238.
JAT96.pdf
• (with H. Berens) Fejer means for multivariate Fourier series, Math. Z. 221 (1996), 449-465.
• (with J. Galambos) Two sets of multivaraite Bonferroni-type inequalities, in Statistical Theory and Applications: Papers in Honor of Herbert A. David, H.N. Nagaraja et. al. eds., Springer-Verlag, New York, 1996, 29-36.
• (with J. Levesly, W. Light, E. W. Cheney) Convolution operators for radial basis approximation, SIAM J. Math. Anal. 27 (1996), 286-304.

1995

• (with T. Sauer) On multivariate Hermite interpolation, Advances in Comp. Math., 4 (1995), 207-259.
• Christoffel functions and Fourier Series for multivariate orthogonal polynomials, J. Approx. Theory, 82 (1995), 205-239.
• (with T. Sauer) A case study in multivariate Lagrange interpolation, in Approximation Theory, Wavelets, and Applications (Maratea, 1994), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 454, Kluwer Acad. Publ., 1995, 443-452.
• (with H. Berens) l-1 Riesz means of the inverse Fourier integral, Approximation Theory VIII, Vol. 1, C.K. Chui and L. Schumaker eds., World Sci. Publ. Co., 1995, 55-62.
• (with P. Vertesi) Mean convergence of Hermite interpolation, revisited. Acta Math. Hungar. 69 (1995), 185-210.
• (with T. Sauer) On multivariate Lagrange interpolation, Math. Comp. 64 (1995), 1147-1170.
• (with H. Berens, H. Schmid) Multivariate Gaussian cubature formula, Arch. Math. 64 (1995), 26-32.
• (with J. Galambos) Bivariate extension of the method of polynomials for Bonferroni-type inequalities, J. Multivariate Analysis, 52 (1995), 131-139.
• (with H. Berens, H. Schmid) On two-dimensional definite orthogonal systems and on lower bound for the number of associated cubature formulas, SIAM J. Math. Anal. 26 (1995), 468-487.

1994

• A Characterization of positive quadrature formulae, Math. Comp. 62 (1994), 703-718.
• Solutions of three-term relation in several variables, Proc. Amer. Math. Soc. 122 (1994), 151-155.
• A class of Bivariate orthogonal polynomials and cubature formula, Numer. Math. 69 (1994), 233-241
• Quasi orthogonal polynomial, quadrature, and interpolation, J. Math. Anal. Appl. 182 (1994), 779-799.
• On zeros of multivariate quasi-orthogonal polynomials and Gaussian cubature formulae, SIAM J. Math. Anal. 25 (1994), 991-1001.
• (with H. Schmid) On bivariable Gaussian cubature formulae, Proc. Amer. Math. Soc. 122 (1994), 833-842.
• Recurrence formula for multivariate orthogonal polynomials, Math. Comp. 62 (1994), 687-702.
• Block Jacobi matrices and zeros of multivariable orthogonal polynomials, Trans. Amer. Math. Soc. 342 (1994), 855-866.
• Multivariable orthogonal polynomials and operator theory, Trans. Amer. Math. Soc. 343 (1994), 193-202.
• (with P. Nevai) Mean convergence of Hermite interpolation, J. Approx. Theory 77 (1994), 282-304.
• (with J. Prestin) Convergence rate of trigonometric interpolant for non-smooth functions, J. Approx. Theory 77 (1994), 113-122.
• Mean convergence of generalized Jacobi series and interpolating polynomials, II, J. Approx. Theory, 76 (1994), 77-92.

1993

• Unbounded commuting operators and multivariate orthogonal polynomials, Proc. Amer. Math. Soc. 119 (1993), 1223-1231.
• On multivariable orthogonal polynomials, SIAM J. Math. Anal. 24 (1993) 783-794.
• Mean convergence of generalized Jacobi series and interpolating polynomials, I, J. Approx. Theory, 72 (1993), 237 -- 251.
• (with D.J. Newman) Tchebycheff polynomials on a trianglular region, Constr. Approx., 9 (1993), 543-546.
• (with E.W. Cheney) A set of research problems in approximation theory, Topics in Polynomials of One and Several Variables and Their Applications, edited by T.M. Rassias, H.M. Srivastava, and A. Yanushanskas, World Scientific Publ., London, 1993, 109-123.
• (with B. Gao) Univariant approximation by superpositions of a sigmoidal function, J. Math. Anal. Appl., 178 (1993), 221-226.
• (with P. Vertesi) Truncated Hermite interpolating polynomials, Studia Sci. Math. Hungar. 28 (1993), 205-213.
• (with E.W. Cheney, W. Light) Constructive methods of approximation by ridge functions and radial functions, Numer. Algorithms. 4 (1993) 205-223.
• (with J. Galambos) Some optimal bivariable Bonferroni-type bounds, Proc. Amer. Math. Soc. 117 (1993), 523-528.

1992

• Gaussian cubature and bivariable polynomial interpolation, Math. Comp. 59 (1992) 547-555.
• (with E.W. Cheney) Strictly positive definite functions on sphere, Proc. Amer. Math. Soc., 116 (1992), 977-981.
• (with E.W. Cheney, W. Light) On kernels and approximation order, Approximation Theory, Lecture Notes in Pure & Applied Math. 138, G. Anastassiou ed. Marcel Dekker, 1992, 227-242.
• (with J. Galambos) Univariant and multivariate Bonferroni-type inequalities: Methods for prrof and questions of optimality, Probability Theory and Applications - in honour of Professor Jorsef Magyorodi, J. Galambos and I. Katai eds. Kluwer Academic Pub. Dordrecht, 1992. p. 155 -164.
• On mean convergence of interpolating polynomials, Approximation theory, Kecskemet, Hungary, Colloq. Math. Soc. Janos Bolyai, 58, 1992, 749-761.
• (with E.W. Cheney) Interpolation by periodic radial functions, Comput. Math. Appl. 24 (1992), 201-215.
• (with H.N. Mhaskar) Hermite interpolation at the zeros of certain Freud-type orthogonal polynomials, Acta Math. Acta Sci. Hungar. 60 (3-4) 1992, 225-240.
• (with H. Berens, H.J. Schmid) Bernstein-Durrmeyer polynomials on a simplex, J. Approx. Theory, 68(1992), 246-260.
• (with P. Vertesi) Weighted L^p convergence of Hermite interpolation of higher order, Acta Math. Acta Sci. Hungar. 59 (1992), 423-438.

1991

• (with H. Berens) K-moduli, moduli of smoothness, and Bernstein polynomials on simplices, Nederl. Akad. Wetensch. Proc. Ser. A, 2 (4), 1991, 411-421.
• The generalized Marcinkiewicz-Zygmund inequality for trigonometric polynomials, J. Mathematical Analysis and Applications, 161(1991) 447-456.
• (with A. Sharma) Mean convergence of trigonometric interpolants on equidistant notes: Birkhoff data, Bulletin of Polish Academy of Sciences, 39(1991), No. 3-4, 199- 206.
• (with H. Berens) On Bernstein-Durrmeyer polynomials with Jacobi weights, Addendum, Approximation, Interpolation, and summation, S. Baron & D. Leviatan eds., Iseral Math. Conf. Proc. 4, Weizmann Science Press of Iseral, Jerusalem 1991, 51-62.
• The Marcinkiewicz-Zygmund inequality wih derivatives, Approx. Theory its Appl., 8(1991), 100-107.
• (with H.N. Mhaskar) Mean convergence of the Freud polynomial expansion, SIAM J. Mathematics Analysis, 22(1991), 847-855.
• Rate of convergence of Hermite-Fejer interpolation of higher order, Progress in Approximation Theory, P. Nevai and A. Pinkus eds. Academic Press, 1991, 893-897; Erratum, J. Approx. Theory, 68(1992), p. 330.
• On the Marcinkiewicz-Zygmund inequality, Progress in Approximation Theory, P. Nevai and A. Pinkus eds. Academic Press, 1991, 879-891.
• On rational Hermite-Fejer type interpolation, Progress in Approximation Theory, P. Nevai and A. Pinkus eds. Academic Press, 1991, 867-877.

1990 --

• (with H. Berens) On Bernstein-Durrmeyer polynomials with Jacobi weights, Approximation Theory and Functional Analysis, C.K.Chui ed. Academic Press, p. 25--46, 1990
• (with J. Galambos) Regularly varying expected residual life and domains of attraction of extreme value distributions, Ann. Univ. Sci. Budapest, Sectio Math. 33(1990), 105-108.
• (with P. Vertesi) Mean convergence of quasi Hermite-Fejer interpolation, Studia Sci. Math. Hungar. 25(1990), 129-145.
• (with J. Galambos) A new method for generating Bonferroni-type inequalities, Math. Proc. of Cambridge Philosophical Society, 107(1990) 601-607.
• (with L. Brutman, P. Vertesi) Interpolation by polynomials in z and z^{-1} on an annulus, IMA J. Numer. Anal. 10(1990), 235-241.
• (with H.N. Mhaskar) The rate of convergence of a Hermite interpolation, Approximation Theory VI, C.K.Chui et al. eds., Academic Press, 433-436,1989.
• On the norm of the Hermite interpolation operator, Approximation Theory VI, C.K.Chui et al. eds., Academic Press, 683-686, 1989.
• (with P. Vertesi) Order of mean convergence of Hermite-Fejer interpolation, Studia Sci. Math. Hungar. 24(1989), 391-401.
• (with X.D. Tan) Some inequalities of Bonferroni-Galambos type, Statistics and Probability Letter, 8(1989), 17-20.
• Bonferroni-type inequalities via interpolating polynomials, Proc. Amer. Math. Soc. 107(1989), 825-831.
• Weight functions for Chebyshev quadrature, Math. Comp., 53(1989), 297-302.
• Existence and uniqueness of polynomial interpolation splines (in Chinese), Numer. Math. J. Chinese Univ. (7)1985, No.3, 271-274.
• A kind of Bezier parametric cubic curves (in Chinese), J. Engineering Math. 2(1985), No.1, 107-112.
• C^3 quintic interpolation splines, (in Chinese), Ibid, no.2, 1985, 69-74.
• Lacunary spline interpolation of even degree, (in Chinese), J. Beijing Inst. Aero. and Astro., no.3, 1984, 93-101.
• Splines of even degree with coefficients expressed by odd order derivatives (in Chinese), Math. Numer. Sinica, 6(1984), 434-438.
• A kind of Hermite-Fejer interpolation polynomials, J. Engineering Math., 2(1985), No.2, 148-154 (in Chinese); English abstract: Kexue Tongbao (A Monthly Journal of Science), 29(1984), 1272-1273.
• Lacunary interpolation splines, J. Computational Math. 2(1984), 41-49.