Preprints & Publications

For my preprints see arxiv

Below is a list of my publications along with links to PDF files. Note that some PDF files may slightly differ from the final version. Please contact me at if you would like to receive a reprint.

  1. Lypaunov's theorem for continuous frames,
    Proc. Amer. Math. Soc. (to appear). PDF
  2. Continuous frames and the Kadison-Singer problem,
    Coherent States and Their Applications - A Contemporary panorama, Springer Proceedings in Physics (to appear). PDF
  3. The Kadison-Singer problem,
    Frames and Harmonic Analysis, Contemp. Math. (to appear). PDF
  4. Improved bounds in Weaver and Feichtinger Conjectures, (with Pete Casazza, Adam Marcus, and Darrin Speegle)
    J. Reine Angew. Math. (to appear). PDF
  5. On Wilson bases in L2(Rd) (with Mads Jakobsen, Jakob Lemvig, and Kasso Okoudjou)
    SIAM J. Math. Anal. 49 (2017), 3999-4023. PDF
  6. The Schur-Horn theorem for unbounded operators with discrete spectrum, (with John Jasper and Bartlomiej Siudeja)
    Bull. London Math. Soc. 49 (2017), 148-164. PDF
  7. Wavelets for non-expanding dilations and the lattice counting estimate (with Jakob Lemvig)
    Int. Math. Res. Not. IMRN 2017, 7264-7291. PDF
  8. Linear independence of time-frequency translates in Rd, (with Darrin Speegle)
    J. Geom. Anal. 26 (2016), 1678-1692. PDF
  9. Diagonals of self-adjoint operators with finite spectrum, (with John Jasper)
    Bull. Polish Acad. Sci. Math. 63 (2015), 249-260. PDF
  10. The structure of translation-invariant spaces on locally compact abelian groups, (with Kenneth Ross)
    J. Fourier Anal. Appl. 21 (2015), 849-884. PDF
  11. A combinatorial characterization of tight fusion frames, (with Kurt Luoto and Ed Richmond)
    Pacific J. Math. 275 (2015), 257-294. PDF
  12. Smooth orthogonal projections on sphere, (with Karol Dziedziul)
    Const. Approx. 41 (2015), 23-48. PDF
  13. Existence of frames with prescribed norms and frame operator, (with John Jasper)
    Excursions in harmonic analysis. Volume 4, 103-117, Appl. Numer. Harmon. Anal., Birkhauser/Springer, New York, 2015. PDF
  14. The Schur-Horn Theorem for operators with finite spectrum, (with John Jasper)
    Trans. Amer. Math. Soc. 367 (2015), 5099-5140. PDF
  15. A mean characterization of weighted anisotropic Besov and Triebel-Lizorkin spaces, (with Baode Li, Dachun Yang, and Wen Yuan)
    Z. Anal. Anwend. 33 (2014), 125-147. PDF
  16. Constructive proof of the Carpenter's Theorem, (with John Jasper)
    Canad. Math. Bull. 57 (2014), 125-147. PDF
  17. Spectra of frame operators with prescribed frame norms, (with John Jasper)
    Harmonic Analysis and Partial Differential Equations, Contemp. Math. 612 (2014), 65-79 . PDF
  18. Littlewood-Paley characterization and duality of weighted anisotropic product Hardy spaces, (with Baode Li and Dachun Yang)
    J. Funct. Anal. 266 (2014), 2611-2661. PDF
  19. Linear independence of time-frequency translates of functions with faster than exponential decay, (with Darrin Speegle)
    Bull. London Math. Soc. 45 (2013), 554-566. PDF
  20. Fourier transform of anisotropic Hardy spaces, (with Li-An Daniel Wang)
    Proc. Amer. Math. Soc. 141 (2013), 2299-2308. PDF
  21. Extrapolation of discrete Triebel-Lizorkin spaces,
    Math. Nachr. 286 (2013), 492-502. PDF
  22. Anisotropic classes of inhomogeneous pseudodifferential symbols, (with Árpád Bényi)
    Collect. Math. 64 (2013), 155-173. PDF
  23. Extension of shift-invariant systems in L2(R) to frames, (with Ole Christensen, Xinli Huang, and Baiyun Yu)
    Numer. Funct. Anal. Optim. 33 (2012), 833-846. PDF
  24. Oversampling of wavelet frames for real dilations, (with Jakob Lemvig)
    J. London Math. Soc. 85 (2012), 765-788. PDF
  25. Duality of weighted anisotropic Besov and Triebel-Lizorkin spaces, (with Baode Li, Dachun Yang, and Wen Yuan)
    Positivity 16 (2012), 213-244. PDF
  26. Orthonormal dilations of non-tight frames, (with John Jasper and Darrin Speegle)
    Proc. Amer. Math. Soc. 139 (2011), 3247-3256. PDF
  27. Characterization of sequences of frame norms, (with John Jasper)
    J. Reine Angew. Math. 654 (2011), 219-244. PDF
  28. Affine and quasi-affine frames for rational dilation, (with Jakob Lemvig)
    Tran. Amer. Math. Soc. 363 (2011), 1887-1924. PDF
  29. Anisotropic singular integrals in product spaces, (with Baode Li, Dachun Yang, and Yuan Zhou)
    Sci. China Math. 53 (2010), 3163-3178. PDF
  30. Anisotropic classes of homogeneous pseudodifferential symbols, (with Árpád Bényi)
    Studia Math. 200 (2010), 41-66. PDF
  31. Weighted anisotropic product Hardy spaces and boundedness of sublinear operators, (with Baode Li, Dachun Yang, and Yuan Zhou)
    Math. Nachr. 283 (2010), 392-442. PDF
  32. Linear independence of Parseval wavelets, (with Darrin Speegle)
    Illinois J. Math. 54 (2010), 771-785. PDF
  33. The closure of the set of tight frame wavelets,
    Acta Appl. Math. 107 (2009), 195-201. PDF
  34. Construction and reconstruction of tight framelets and wavelets via matrix mask functions, (with Ziemowit Rzeszotnik)
    J. Funct. Anal. 256 (2009), 1065-1105. PDF
  35. Intersection of dilates of shift-invariant spaces,
    Proc. Amer. Math. Soc. 137 (2009), 563-572. PDF
  36. Dimension functions of rationally dilated GMRAs and wavelets, (with Kenneth Hoover)
    J. Fourier Anal. Appl. 15 (2009), 585-615. PDF
  37. Weighted anisotropic Hardy spaces and their applications in boundedness of sublinear operators, (with Baode Li, Dachun Yang, and Yuan Zhou)
    Indiana Univ. Math. J. 57 (2008), 3065-3100. PDF
  38. Baggett's problem for frame wavelets,
    Representations, wavelets, and frames, 153-173, Appl. Numer. Harmon. Anal., Birkhauser Boston, Boston, MA, 2008. PDF
  39. Duality and interpolation of anisotropic Triebel-Lizorkin spaces,
    Math. Z. 259 (2008), 131-169. PDF
  40. Anisotropic Triebel-Lizorkin spaces with doubling measures,
    J. Geom. Anal. 17 (2007), 387-424. PDF
  41. The canonical and alternate duals of a wavelet frame, (with Jakob Lemvig)
    Appl. Comput. Harmon. Anal. 23 (2007), 263-272. PDF
  42. Characterization and perturbation of Gabor frame sequences with rational parameters, (with Ole Christensen)
    J. Approx. Theory 147 (2007), 67-80. PDF
  43. The structure of shift-modulation invariant spaces: the rational case
    J. Funct. Anal. 244 (2007), 172-219. PDF
  44. Connectivity and density in the set of framelets
    Math. Res. Lett. 14 (2007), 285-293. PDF
  45. Duals of Hardy spaces on homogeneous groups (with Gerald B. Folland)
    Math. Nachr. 280 (2007), 1223-1229. PDF
  46. Minimal generator sets for finitely generated shift-invariant subspaces of L2(Rn), (with Norbert Kaiblinger)
    J. Math. Anal. Appl. 313 (2006), 342-352. PDF
  47. The Feichtinger conjecture for wavelet frames, Gabor frames and frames of translates, (with Darrin Speegle)
    Canad. J. Math. 58 (2006), 1121-1143. PDF
  48. Atomic and molecular decompositions of anisotropic Triebel-Lizorkin spaces, (with Kwok-Pun Ho)
    Trans. Amer. Math. Soc. 358 (2006), 1469-1510. PDF
  49. On the existence of multiresolution analysis for framelets (with Ziemowit Rzeszotnik),
    Math. Ann. 332 (2005), 705-720. PDF
  50. Atomic and molecular decompositions of anisotropic Besov spaces,
    Math. Z. 250 (2005), 539-571. PDF
  51. Erratum to: Atomic and Molecular Decompositions of Anisotropic Besov Spaces,
    Math. Z. 273 (2013), 1297-1299. PDF
  52. Boundedness of operators on Hardy spaces via atomic decompositions,
    Proc. Amer. Math. Soc. 133 (2005), 3535-3542. PDF
  53. The spectral function of shift-invariant spaces on general lattices, (with Ziemowit Rzeszotnik)
    Wavelets, frames and operator theory, Contemp. Math. 345 (2004), 49-59. PDF
  54. Biorthogonal wavelets, MRA's and shift-invariant spaces, (with Gustavo Garrigós)
    Studia Math. 160 (2004), 231-248. PDF
  55. Affine Frames, GMRA's, and the Canonical Dual, (with Eric Weber)
    Studia Math. 159 (2003), 453-479. PDF
  56. Riesz wavelets and generalized multiresolution analyses,
    Appl. Comput. Harmon. Anal. 14 (2003), 181-194. PDF
  57. The spectral function of shift-invariant spaces, (with Ziemowit Rzeszotnik)
    Michigan Math. J. 51 (2003), 387-414. PDF
  58. Quasi-affine systems and the Calderòn condition,,
    Harmonic Analysis at Mount Holyoke, Contemp. Math. 320 (2003), 29-43. PDF
  59. Anisotropic Hardy spaces and wavelets,
    Mem. Amer. Math. Soc. 164 (2003), no. 781, 122pp. PDF
  60. On a problem of Daubechies,
    Constr. Approx. 19 (2003), 179-190. PDF
  61. The wavelet dimension function for real dilations and dilations admitting non-MSF wavelets, (with Darrin Speegle)
    Approximation Theory X: Wavelets, Splines, and Applications, 63-85, Vanderbilt University Press, 2002. PDF
  62. Meyer type wavelet bases in R2, (with Darrin Speegle)
    J. Approx. Theory 116 (2002), 49-75. PDF
  63. Combined MSF multiwavelets,
    J. Fourier Anal. Appl. 8 (2002), 201-210. PDF
  64. The construction of r-regular wavelets for arbitrary dilations,
    J. Fourier Anal. Appl. 7 (2001), 489-506. PDF
  65. On characterizations of multiwavelets in L2(Rn),
    Proc. Amer. Math. Soc. 129 (2001), 3265-3274. PDF
  66. A characterization of dimension functions of wavelets, (with Ziemowit Rzeszotnik and Darrin Speegle)
    Appl. Comput. Harmon. Anal. 10 (2001), 71-92. PDF
  67. Inverse volume inequalities for matrix weights,
    Indiana Univ. Math. J. 50 (2001), 383-410. PDF
  68. The structure of shift invariant subspaces of L2(Rn),
    J. Funct. Anal. 177 (2000), 282-309. PDF
  69. A characterization of affine dual frames in L2(Rn),
    Appl. Comput. Harmon. Anal. 8 (2000), 203-221. PDF
  70. Tight frames of multidimensional wavelets,
    J. Fourier Anal. Appl. 3 (1997), 525-542. PDF