Publications of Yuan Xu
Books
 (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: 9781461466598 (Print) 9781461466604 (Online).
Errata
 (with Charles F. Dunkl) "Orthogonal Polynomials of Several Variables",
Encyclopedia of Mathematics and its Applications, vol. 81,
Cambridge Univ. Press, ISBN 0521800439, 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 hharmonics and Dunkl Transforms,
Advanced Courses in Mathematics  CRM Barcelona,
Birkhauser, 2015.
ISBN 9783034808873.
 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. 141196. W. zu Castell, F. Filbir, B. Forster (eds.), Nova Science
Publishers, 2005. Inzell.pdf
Book chapter
 Orthogonoal polynomials of several variables. Chapter 2 of
Encyclopedia of Special Functions: The AskeyBateman Project. Volume 2.
Multivariable Special Functions,
Cambridge Univ. Press, 2021, pp 1978.
ABChapt2
Edited In Memorianm
 In Memorian of Donald Newman (1930  2007).
J. Approx. Theory, 154 (2008), 3758.
DJN
 In Memorian of Borislav D. Bojanov (1944  2009).
J. Approx. Theory, 162 (2010), 17391765.
(coedited with A. Kroo and A. Pinkus)
Bojanov
 In Memorian of Hubert A. Berens (1936  2015).
J. Approx. Theory, 198 (2015), ivxxix.
Berens
 In Memorian of Ward Cheney (1929  2016).
J. Approx. Theory, 213 (2017), ivxxxii.
(coedited with Dany Leviatan)
Cheney
Papers
Submitted

Maximal functions and multiplier theorem for Fourier orthogonal series.
MaximalFunc

(with P. Iliev) Hahn polynomials for hypergeometric distribution.
HDHahn
Accepted

Approximation and localized polynomial frame on double hyperbolic and
conic domains.
Constructive Approx.
ConicDomainsII

Fourier orthogonal series on a paraboloid.
J. d'Analyse Math.
Paraboloid

(with M. Fasondini, S. Olver)
Orthogonal structure on a cubic planar curve.
Found. Comput. Math.
OPcubic
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.
Vsymmetry

(with S. Olver) Nonhomogeneous wave equation on a cone.
Integral Transforms Spec Funct. 32 (2001), 604619.
waveeqn

Orthogonal structure and orthogonal series in and on a double cone
or a hyperboloid.
Trans. Amer. Math. Soc. 374 (2021), 36033657.
hyperboloid

(with S. Olver) Orthogonal structure on a quadratic curve.
IMA J. Numer. Anal. 41 (2021), 206246.
OPquadratic
2020

Intertwining operators associated to dihedral groups.
Constr. Approx. 52 (2020), 395422.
VDihedral

(with S. Olver)
Orthogonal polynomials in and on a quadratic surface of revolution
Math. Comp. 89 (2020), 28472865.
OPsurface

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.
Hahnpolyhedra

(with G. Kerkyacharian and P. Petrushev)
Gaussian bounds for the heat kernels on the ball and simplex:
classical approach.
Studia Math. 250 (2020), 235252.
HeatKernel2

(with G. Kerkyacharian and P. Petrushev)
Gaussian bounds for the weighted heat kernels on the interval, ball and
simplex.
Constr. Approx. 51 (2020), 73122.
HeatKernel
2019

(with D. Dimitrov)
Wronskians of Fourier and Laplace transforms.
Trans. Amer. Math. Soc. 372 (2019), 41074125.
WFLT

(with S. Olver) Orthogonal structure on a wedge and on the boundary
of a square.
Found. Comp. Math. (FoCM) 19 (2019), 561589.
OPwedge

(with H. Feng and C. Krattenthaler) Best polynomial approximation on the
triangle.
J. Approx. Theory 241 (2019), 6378.
BestAppTriangle
2018

Approximation by polynomials in Sobolev spaces with Jacobi weight.
J. Fourier Anal. Appl. 24 (2018) 14381459.
1DApprox

(with M. Pinar)
Best polynomial approximation on the unit ball.
IMA J. Numer. Anal. 38 (2018), 12091228,
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. 12871305, Springer, Cham, 2018.
Cubasquare

(with N. Proudfoot and B. Young) The Zpolynomial of a matroid.
Electon. J. Combin.
25 (2018) no. 1, Paper 1.26.
Zpolynomials

Positive definite functions on the unit sphere and integrals of
Jacobi polynomials.
Proc. Amer. Math. Soc. 146 (2018), 20392048.
PDFJacobi
2017

Approximation and orthogonality in Sobolev spaces on a triangle.
Constr. Approx. 46 (2017), 349434.
ApproxTriangle

(with P. Iliev) Connection coefficients of classical orthogonal polynomials
of several variables.
Adv. Math. 310 (2017), 290306.
ConnCoeff

Minimal Cubature rules and polynomial interpolation in two variables II.
J. Approx. Theory 214 (2017), 4968.
Cuba2d2
2016

Positivity and Fourier integral on hexagonal domain.
J. Approx. Theory 207 (2016), 193206.
PosFourier

(with D. Dimitrov)
Slater determinants of orthogonal polynomials.
J. Math. Anal. Appl. 435 (2016), 15521572.
DetOP
 Orthogonal expansions for generalized Gegenbauer weight function on the unit ball.
Contemp. Math., Vol. 661, 2016, 153165.
GGball
2015
 An intergral identity with applications in orthogonal polynomials.
Proc. Amer. Math. Soc. 143 (2015), 52535263.
ReprodKernel
 Generalized characteristic polynomials and Gaussian cubature rules.
SIAM. J. Matrix Anal. 36 (2015), 11291142.
OPzero
 (with F. Marcellan)
On Sobolev orthogonal polynomials.
Expos. Math. 33 (2015), 308352.
SOP
 Hahn, Jacobi, and Krawtchouck polynomials of several variables.
J. Approx. Theory 195 (2015), 1942.
HJK
 (with L. Fernandez, F. Marcellan, T. Perez, M. Pinar)
Sobolev orthogonal polynomials on product domains.
J. Comp. Appl. Math. 284 (2015), 202215.
ProdSOP
 Uncertainty principles for weighted spheres, balls and simplexes.
J. Approx. Theory 192 (2015), 193214.
WeightedUncert
 Complex versus real orthogonal polynomials of two variables.
Integral Trans. & Special Funct. 26 (2015) 134151.
ComplexOP
2014
 (with H. Li) Spectral approximation on the unit ball.
SIAM J. Numer. Anal. 52 (2014), 26472675.
SpectralApprox
 Best polynomial approximation on unit sphere and unit ball.
In Approximation Theory XIV: San Antonio 2013 ,
Springer Proceedings in Mathematics, Springer, p. 357375.
SanAntonio

(with F. Dai)
HardyRellich inequality and uncertainty principle on the unit sphere.
Constr. Approx. 40 (2014), 141171.
Uncertainty

(with R.K. Beatson, W. zu Castell)
A Polya criterion for (strict) positive definiteness on the sphere.
IMA J. Numer. Anal. 34 (2014), 550568.
pdfsphere
 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), 12511277.
CubaSimplex
2013

(with R. Aktas)
Sobolev orthogonal polynomials on a simplex.
Int. Math. Res. Notice, , 2013 (2013), no. 13, 30873131.
SOPsimplex
 (with T. E. Perez, M. A. Pinar)
Weighted Sobolev orthogonal polynomials on the unit ball,
J. Approx. Theory 171 (2013), 84104.
SOPball

Minimal cubature rules on an unbounded domain.
Dolomite Res. Notes on Approximation 6 (2013), 38.
UnbddDomain

(with B. Rider and C. D. Sinclair)
A solvable mixed charge ensemble on the line: global results.
Prob. Theory & Related Fields. 155 (2013), 127164.
Twocharge
2012

Orthogonal polynomials and expansions for a family of weight functions
in two variables.
Constr. Approx. 36 (2012), 161190.
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 CliffordFourier 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), 14001418.
Sobolev

On GaussLobatto integration on the triangle.
SIAM J. Numer. Anal. 49 (2011), 541548.
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), 115138.
AppHexagon

(with H. Li and J. Sun)
Discrete Fourier analysis with lattices on planar domains.
Numer. Algorithm 55 (2010), 279300.
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 dvariables.
J. Fourier Anal. Appl. 16 (2010), 383  433.
Ad Lattice

(with K. Ivanov and P. Petrushev)
Subexponentially localized kernels and frames induced by
orthogonal expansions. Math. Z. 264 (2010), 361  397.
Subexp

(with L. Fernandez, T. Perez, M. Pinar)
Kralltype orthogonal polynomials in several variables.
J. Comp. Appl. Math. 233 (2010), 15191524.
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 IllPosed 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) 167179.
Biangle

(with M. Pinar) Orthogonal polynomials and partial differential
equations on the unit ball.
Proc. Amer. Math. Soc. 137 (2009), 2979  2987.
OPPDE

(with A. M. Delgado, J. S. Geronimo, P. Iliev)
On a two variable class of BernsteinSzego measures,
Constr. Approx. 30 (2009), 71 91.
BS

(with H. Li) Discrete Fourier Analysis on a dodecahedron
and a tetrahedron, Math. Comp. 78 (2009), 9991029.
Dodeca
 (with G. Kerkyacharian, P. Petrushev, and D. Picard)
Decomposition of TriebelLizorkin and Besov spaces in the context
of Laguerre expansions. J. Functional Anal. 256 (2009), 11371188.
Lagurerre
 (with H. Li and J. Sun)
Cubature formula and interpolation on the cubic domain.
Numer. Math. Theory Methods Appl. 2 (2009), 119152.
Cubic
 (with S. De Marchi and M. Vianello)
New cubature formulae and hyperinterpolation in three variables.
BIT Numer. Math. 49 (2009), 5573.
3dcubature

(with Feng Dai) Cesaro means of orthogonal expansions in several variables,
Constr. Approx. 29 (2009), 129155.
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 TriebelLizorkin
and Besov spaces on the ball,
Proc. London Math. Soc. 97 (2008), 477513.
KPX2

(with B. Kroetz and S. Thangavelu)
Heat transform for nilmanifolds associated to the Heisenberg group,
Revista Mat. Iberoamericana, 24 (2008) 243266.
KTX2

Sobolev orthogonal polynomials defined via gradient on
the unit ball, J. Approx. Theory. 152 (2008), 5265.
SobolevOP_II

(with P. Petrushev) Decomposition of spaces of distributions induced
by Hermite expansions,
J. Fourier. Anal. Appl. 14 (2008), 372414.
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), 16531681.
LSX

(with G. Kyriazis and P. Petrushev)
Jacobi decomposition of weighted TriebelLizorkin and Besov spaces,
Studia Math. 186 (2008), 161202.
Jacobi_II

(with H. de las Heras, O. Tischenko and C. Heoschen)
Comparison of the interpolation functions to improve a rebinningfree
CTreconstruction algorithm,
Z. Med. Physik 18 (2008), 716.
ZMP

(with P. Petrushev) Localized polynomial kernels and
frames on the ball,
Constr. Approx. 27 (2008) 121148.
PX2
SPIE Proceedings

(with H. de las Heras, O. Tischenko, B. Renger and C. Heoschen)
Experimental proof of an idea for a CTscanner 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), 477504.
MaximalFunc

(with L. Bos, S. De Marchi and M. Vianello)
Bivariate Lagrange interpolation at Padua points: the ideal theory
approach, Numer. Math., 108 (2007), 4357.
Paduva2

(with O. Tischenko)
Fast OPED algorithm for reconstruction of images from Radon data,
East. J. Approx. 12 (2007), 427444.
FastOPED

Reconstruction from Radon projections and orthogonal expansion on a ball,
J. Physics A: Math. and Theor., 40 (2007) 72397253.
Radon2

(with O. Tischenko, C. Hoeschen) Image reconstruction by
OPED algorithm with averaging, Numer. Algo. 45 (2007), 179193.
OPEDave

(with P. Iliev) Discrete orthogonal polynomials and
difference equations of several variables, Adv. in Math.,
212 (2007) 136.
Difference

(with O. Tischenko and C. Heoschen)
Approximation and reconstruction from attenuated Radon projections,
SIAM J. Numer. Anal., 45 (2007), 108132.
Attenuated

(with W. Castell and F. Lain Fernandez)
Polynomial interpolation on the unit sphere II,
Adv. in Comp. Math.
26 (2007), 155171.
Interpolation II

(with S. Thangavelu) Riesz transform and singular integrals
for Dunkl transform, J. Comp. Appl. Math.
199 (2007), 181195.
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,
61425L.
 (H. de las Heras, O. Tischenko, W. Panzera, Y. Xu and C. Heoschen)
Modelling and testing of a nonstandard scanning device with
dose reduction potential,
Proc. SPIE, Vol. 6142, Medical Imaging 2007: Physics of Medical Imaging,
61423R.
2006

Analysis on the unit ball and on the simplex,
Elec. Trans. Numer. Anal. 25 (2006), 284301.
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) 1525.
Padua1

A new approach to the reconstruction of images from Radon
projections, Adv. in Applied Math. 36 (2006), 388420.
Radon

A family of Sobolev orthogonal polynomials on the unit ball,
J. Approx. Theory 138 (2006), 232241.
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. 791798.

(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. 893899.
2005

(with S. Thangavelu)
Generalized translation and convolution operator for Dunkl transform,
J. d'Analyse Mathematique 97 (2005) 2556.
Dunkl transform

( with B. Bojanov) Reconstruction of a polynomial
from its Radon projections, SIAM J. Math. Anal. 37 (2005), 238250.
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) 449475.
Difference

Rodrigues type formula for orthogonal polynomials on the unit ball,
Proc. Amer. Math. Soc. 133 (2005), 19651976.
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), 301336.
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 1623, 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. 12, 119147.
VertesiXu

Generalized translation operator and approxiamtion 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. 489512.
Transl JCAM.pdf

Monomial orthogonal polynomials of several variables, J. Approx. Theory,
133 (2005), 137. Preprint, May, 2002.
Monomial.pdf

Weighted approximation of functions on the unit sphere,
Const. Approx., 21 (2005), 128. Preprint, July 2002.
Bestapp
2004

On Discrete orthogonal polynomials of several variables,
Adv. in Applied Math., 33 (2004), 615632.
Discrete

On polynomials of least deviation from zero in several variables,
J. Experimental Math. 13 (2004), 103112.
Least,
revised Least.pdf

Approximation by means of hharmonics polynomials on the unit sphere,
Adv. in Comp. Math., 20 (2004), 247260.
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. 325337.
ballinter.pdf

Polynomial interpolation on the unit sphere and on the unit ball,
Adv. in Comp. Math., 20 (2004), p. 247260.
ACMinterp.ps.gz
2003

Polynomial interpolation on the unit sphere, SIAM J. Numer. Anal.,
41 (2003), p. 751766.
InterSph.ps.gz
 (with Zhongkai Li) Summability of orthogonal expansions of several
variables, J. Approx. Theory, 122 (2003), 267333.
LiXu.ps.gz

Lower bound for the number of nodes of cubature formulae on the unit ball,
J. Complexity, 19 (2003), 392402.
CFbound.ps.gz

Orthogonal expansions and weighted approximation on the unit
sphere, Constructive Function Theory, DARBA, Sofia, 2003, p. 156177.
Varna.ps.gz
 (with B. Bojanov) Polynomial interpolation of two variables
based on a factorization method. J. Approx. Theory,
120 (2003), 267282.
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), 54995510.
Biortho.ps.gz
 (with B. Bojanov) On a Hermite interpolation by polynomials
of two variables, SIAM. J. Numer. Anal., 39 (2002), 17801793.
BoXu1.ps.gz
2001
 Representation of reproducing kernels and the Lebesgue
constants on the ball, J. Approx. Theory, 112 (2001), 295310.
Reprod.ps.gz
 Orthogonal polynomials and summability on spheres and on balls,
Math. Proc. Cambridge Phil. Soc., 31 (2001), 139155.
BallSph
 (with Hubert Berens, Zhongkai Li) On l1 Riesz
summability of the inverse Fourier integral, Indag. Math.,
12 (2001), 4153. BLX.ps.gz
 Orthogonal polynomials on the ball and on the simplex for weight
functions with reflection symmetries, Const. Approx.,
17 (2001), 383412.
Classical.ps.gz
 (wiht S. Heo) Constructing cubature formulae for sphere and
triangle, Math. Comp., 70 (2001), 269279.
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), 349368.
OPCF.ps.gz
2000
 (with S. Heo) Invariant cubature formulae for spheres and
balls by combinatorial methods, SIAM J. Numer. Anal., 38 (2000),
626638.
HeoXu.pdf
 A note on summability of Laguerre expansions,
Proc. Amer. Math. Soc.,
128 (2000), 35713578.
Laguerre.ps.gz
 A product formula for Jacobi polynomials, in Special Functions,
Proceedings of International Workshop, Hong Kong, June 2125, 1999, World
Sci. Publ., 2000, p. 423430.
Intertw.ps.gz
 Harmonic polynomials associated with reflection groups,
Can. Math. Bulletin, 43 (2000), 496507.
Harmon.ps.gz
 FunkHecke formulae for orthogonal polynomials on sphere and on balls,
Bull. London Math. Soc., 32 (2000), 447457.
FunkHecke.ps.gz
 (with Zhongkai Li) Summability of the product Jacobi series,
J. Approx. Theory, 104 (2000), 287301.
LiXu.ps.gz
 Polynomial interpolation in several variables, cubature formulae,
and ideals, Advances in Comp. Math., 12 (2000), 363376.
Interpo.ps.gz
 Constructing cubature formulae by the method of reproducing kernel,
Numer. Math., 85 (2000), 155173.
ReprodCF.ps.gz
1999
 Cubature formula and polynomial ideals, Advances in Applied Math.,
23 (1999), 211233.
 (with S. Heo) Constructing cubature formulae for spheres and balls,
J. Comp. Appl. Math. 112 (1999), 95119.
 Aymptotics of the Christoffel functions on a simplex in R^d,
J. Approx. Theory, 99 (1999), 122133.
 (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, 203221.
 Summability of Fourier orthogonal series for Jacobi weight on a ball
in R^d, Trans. Amer. Math. Soc., 351 (1999), pp. 24392458.
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), 30273036.
 Orthogonal polynomials and cubature formulae on spheres and on simplices,
Methods Anal. and Appl., 5 (1998), p. 169184.
Simplex.pdf
 Minimal Cubature formulae for a family of radial weight functions,
Advances in Comp. Math., 8 (1998), 367380.
 Intertwining operator and hharmonics associated with reflection
group, Canadian J. Math., 50 (1998), 193209.
 Orthogonal polynomials and cubature formulae on spheres and on balls,
SIAM J. Math. Anal., 29 (1998), 779793.
SIAMsphere.pdf
1997
 Integration of the intertwining operator for hharmonic polynomials
associated to reflection groups, Proc. Amer. Math. Soc.,
125 (1997), 2963297.
 (with H. Berens, M. Finzel, W. Li) Hoffman's error bounds and uniform
Lipschitz continuity of Best l_papproximations, J. Math. Anal. Appl.
, 213 (1997), 183201.
 Orthogonal polynomials for a family of product weight functions on
the spheres, Canadian J. Math., 49 (1997), 175192.
Sphere.ps.gz
 (with H. Berens) l1 summability for multivariate Fourier integrals
and positivity, Math. Proc. Cambridge Phil. Soc.
122 (1997), 149172.
 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), 623638.
 On orthogonal polynomials in several variables, Special Functions,
qsereis and Related Topics, The Fields Institute for Research
in Mathematical Sciences, Communications Series, Volume 14, 1997, p. 247270
fields.pdf
 On commuting family of block Jacobi matrices, Comput. Math. Appl.
33 (1997), 211222.
1996
 Asymptotics for orthogonal polynomials and Christoffel functions on
a ball, Methods and Appl. Analysis, 3 (1996), 257272.
 (with T. Sauer) Regular points for Lagrange interpolation on the unit
disk, Numer. Algorithm, 12 (1996), p. 287296.
 Lagrange interpolation on Chebyshev points of two variables, J. Approx.
Theory, 87 (1996), p. 220238.
JAT96.pdf
 (with H. Berens) Fejer means for multivariate Fourier series, Math.
Z. 221 (1996), 449465.
 (with J. Galambos) Two sets of multivaraite Bonferronitype inequalities,
in Statistical Theory and Applications: Papers in Honor of Herbert A.
David, H.N. Nagaraja et. al. eds., SpringerVerlag, New York, 1996, 2936.
 (with J. Levesly, W. Light, E. W. Cheney) Convolution operators
for radial basis approximation, SIAM J. Math. Anal. 27 (1996), 286304.
1995
 (with T. Sauer) On multivariate Hermite interpolation, Advances in
Comp. Math., 4 (1995), 207259.
 Christoffel functions and Fourier Series for multivariate orthogonal
polynomials, J. Approx. Theory, 82 (1995), 205239.
 (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,
443452.
 (with H. Berens) l1 Riesz means of the inverse Fourier integral,
Approximation Theory VIII, Vol. 1, C.K. Chui and L. Schumaker eds.,
World Sci. Publ. Co., 1995, 5562.
 (with P. Vertesi) Mean convergence of Hermite interpolation,
revisited. Acta Math. Hungar. 69 (1995), 185210.
 (with T. Sauer) On multivariate Lagrange interpolation, Math. Comp.
64 (1995), 11471170.
 (with H. Berens, H. Schmid) Multivariate Gaussian cubature formula,
Arch. Math. 64 (1995), 2632.
 (with J. Galambos) Bivariate extension of the method of polynomials
for Bonferronitype inequalities, J. Multivariate Analysis, 52 (1995),
131139.
 (with H. Berens, H. Schmid) On twodimensional definite orthogonal
systems and on lower bound for the number of associated cubature formulas,
SIAM J. Math. Anal. 26 (1995), 468487.
1994
 A Characterization of positive quadrature formulae, Math. Comp. 62
(1994), 703718.
 Solutions of threeterm relation in several variables, Proc. Amer.
Math. Soc. 122 (1994), 151155.
 A class of Bivariate orthogonal polynomials and cubature formula,
Numer. Math. 69 (1994), 233241
 Quasi orthogonal polynomial, quadrature, and interpolation, J. Math.
Anal. Appl. 182 (1994), 779799.
 On zeros of multivariate quasiorthogonal polynomials and Gaussian
cubature formulae, SIAM J. Math. Anal. 25 (1994), 9911001.
 (with H. Schmid) On bivariable Gaussian cubature formulae, Proc.
Amer. Math. Soc. 122 (1994), 833842.
 Recurrence formula for multivariate orthogonal polynomials,
Math. Comp.
62 (1994), 687702.
 Block Jacobi matrices and zeros of multivariable orthogonal polynomials,
Trans. Amer. Math. Soc. 342 (1994), 855866.
 Multivariable orthogonal polynomials and operator theory, Trans. Amer.
Math. Soc. 343 (1994), 193202.
 (with P. Nevai) Mean convergence of Hermite interpolation, J.
Approx. Theory 77 (1994), 282304.
 (with J. Prestin) Convergence rate of trigonometric interpolant for
nonsmooth functions, J. Approx. Theory 77 (1994), 113122.
 Mean convergence of generalized Jacobi series and interpolating
polynomials, II, J. Approx. Theory, 76 (1994), 7792.
1993
 Unbounded commuting operators and multivariate orthogonal polynomials,
Proc. Amer. Math. Soc. 119 (1993), 12231231.
 On multivariable orthogonal polynomials, SIAM J. Math. Anal. 24
(1993) 783794.
 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), 543546.
 (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, 109123.
 (with B. Gao) Univariant approximation by superpositions of a
sigmoidal function, J. Math. Anal. Appl., 178 (1993), 221226.
 (with P. Vertesi) Truncated Hermite interpolating polynomials,
Studia Sci. Math. Hungar. 28 (1993), 205213.
 (with E.W. Cheney, W. Light) Constructive methods of approximation
by ridge functions and radial functions, Numer. Algorithms. 4 (1993)
205223.
 (with J. Galambos) Some optimal bivariable Bonferronitype bounds,
Proc. Amer. Math. Soc. 117 (1993), 523528.
1992
 Gaussian cubature and bivariable polynomial interpolation,
Math. Comp. 59 (1992) 547555.
 (with E.W. Cheney) Strictly positive definite functions on sphere,
Proc. Amer. Math. Soc., 116 (1992), 977981.
 (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, 227242.
 (with J. Galambos) Univariant and multivariate Bonferronitype
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, 749761.
 (with E.W. Cheney) Interpolation by periodic radial functions,
Comput. Math. Appl. 24 (1992), 201215.
 (with H.N. Mhaskar) Hermite interpolation at the zeros of certain
Freudtype orthogonal polynomials, Acta Math. Acta Sci. Hungar. 60 (34)
1992, 225240.
 (with H. Berens, H.J. Schmid) BernsteinDurrmeyer polynomials
on a simplex, J. Approx. Theory, 68(1992), 246260.
 (with P. Vertesi) Weighted L^p convergence of Hermite
interpolation of higher order, Acta Math. Acta Sci. Hungar.
59 (1992), 423438.
1991
 (with H. Berens) Kmoduli, moduli of smoothness, and Bernstein
polynomials on simplices, Nederl. Akad. Wetensch. Proc. Ser. A, 2 (4),
1991, 411421.
 The generalized MarcinkiewiczZygmund inequality for trigonometric
polynomials, J. Mathematical Analysis and Applications, 161(1991) 447456.
 (with A. Sharma) Mean convergence of trigonometric interpolants
on equidistant notes: Birkhoff data, Bulletin of Polish Academy of Sciences,
39(1991), No. 34, 199 206.
 (with H. Berens) On BernsteinDurrmeyer 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, 5162.
 The MarcinkiewiczZygmund inequality wih derivatives, Approx. Theory
its Appl., 8(1991), 100107.
 (with H.N. Mhaskar) Mean convergence of the Freud polynomial
expansion, SIAM J. Mathematics Analysis, 22(1991), 847855.
 Rate of convergence of HermiteFejer interpolation of higher order,
Progress in Approximation Theory, P. Nevai and A. Pinkus eds. Academic
Press, 1991, 893897; Erratum, J. Approx. Theory, 68(1992), p. 330.
 On the MarcinkiewiczZygmund inequality, Progress in Approximation Theory,
P. Nevai and A. Pinkus eds. Academic Press, 1991, 879891.
 On rational HermiteFejer type interpolation, Progress in Approximation
Theory, P. Nevai and A. Pinkus eds. Academic Press, 1991, 867877.
1990 
 (with H. Berens) On BernsteinDurrmeyer polynomials with Jacobi
weights, Approximation Theory and Functional Analysis, C.K.Chui ed. Academic
Press, p. 2546, 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), 105108.
 (with P. Vertesi) Mean convergence of quasi HermiteFejer
interpolation, Studia Sci. Math. Hungar. 25(1990), 129145.
 (with J. Galambos) A new method for generating Bonferronitype
inequalities, Math. Proc. of Cambridge Philosophical Society, 107(1990)
601607.
 (with L. Brutman, P. Vertesi) Interpolation by polynomials
in z and z^{1} on an annulus, IMA J. Numer. Anal. 10(1990), 235241.
 (with H.N. Mhaskar) The rate of convergence of a Hermite
interpolation, Approximation Theory VI, C.K.Chui et al. eds., Academic Press,
433436,1989.
 On the norm of the Hermite interpolation operator, Approximation Theory
VI, C.K.Chui et al. eds., Academic Press, 683686, 1989.
 (with P. Vertesi) Order of mean convergence of HermiteFejer
interpolation, Studia Sci. Math. Hungar. 24(1989), 391401.
 (with X.D. Tan) Some inequalities of BonferroniGalambos type,
Statistics and Probability Letter, 8(1989), 1720.
 Bonferronitype inequalities via interpolating polynomials, Proc. Amer.
Math. Soc. 107(1989), 825831.
 Weight functions for Chebyshev quadrature, Math. Comp., 53(1989), 297302.
 Existence and uniqueness of polynomial interpolation splines (in Chinese),
Numer. Math. J. Chinese Univ. (7)1985, No.3, 271274.
 A kind of Bezier parametric cubic curves (in Chinese), J. Engineering
Math. 2(1985), No.1, 107112.
 C^3 quintic interpolation splines, (in Chinese), Ibid, no.2, 1985,
6974.
 Lacunary spline interpolation of even degree, (in Chinese), J. Beijing
Inst. Aero. and Astro., no.3, 1984, 93101.
 Splines of even degree with coefficients expressed by odd order derivatives
(in Chinese), Math. Numer. Sinica, 6(1984), 434438.
 A kind of HermiteFejer interpolation polynomials, J. Engineering
Math., 2(1985), No.2, 148154 (in Chinese); English abstract: Kexue Tongbao
(A Monthly Journal of Science), 29(1984), 12721273.
 Lacunary interpolation splines, J. Computational Math. 2(1984), 4149.