Preprints & Publications

Below is a list of my preprints along with links to PDF files.

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. Improved bounds in Weaver and Feichtinger Conjectures, (with Pete Casazza, Adam Marcus, and Darrin Speegle)
    J. Reine Angew. Math. (to appear). PDF
  2. Linear independence of time-frequency translates in Rd, (with Darrin Speegle)
    J. Geom. Anal. 26 (2016), 1678-1692. PDF
  3. Diagonals of self-adjoint operators with finite spectrum, (with John Jasper)
    Bull. Polish Acad. Sci. Math. 63 (2015), 249-260. PDF
  4. The structure of translation-invariant spaces on locally compact abelian groups, (with Kenneth Ross)
    J. Fourier Anal. Appl. 21 (2015), 849-884. PDF
  5. A combinatorial characterization of tight fusion frames, (with Kurt Luoto and Ed Richmond)
    Pacific J. Math. 275 (2015), 257-294. PDF
  6. Smooth orthogonal projections on sphere, (with Karol Dziedziul)
    Const. Approx. 41 (2015), 23-48. PDF
  7. 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
  8. The Schur-Horn Theorem for operators with finite spectrum, (with John Jasper)
    Trans. Amer. Math. Soc. 367 (2015), 5099-5140. PDF
  9. 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
  10. Constructive proof of the Carpenter's Theorem, (with John Jasper)
    Canad. Math. Bull. 57 (2014), 125-147. PDF
  11. Spectra of frame operators with prescribed frame norms, (with John Jasper)
    Harmonic Analysis and Partial Differential Equations, Contemp. Math. 612 (2014), 65-79 . PDF
  12. 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
  13. 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
  14. Fourier transform of anisotropic Hardy spaces, (with Li-An Daniel Wang)
    Proc. Amer. Math. Soc. 141 (2013), 2299-2308. PDF
  15. Extrapolation of discrete Triebel-Lizorkin spaces,
    Math. Nachr. 286 (2013), 492-502. PDF
  16. Anisotropic classes of inhomogeneous pseudodifferential symbols, (with Árpád Bényi)
    Collect. Math. 64 (2013), 155-173. PDF
  17. 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
  18. Oversampling of wavelet frames for real dilations, (with Jakob Lemvig)
    J. London Math. Soc. 85 (2012), 765-788. PDF
  19. Duality of weighted anisotropic Besov and Triebel-Lizorkin spaces, (with Baode Li, Dachun Yang, and Wen Yuan)
    Positivity 16 (2012), 213-244. PDF
  20. Orthonormal dilations of non-tight frames, (with John Jasper and Darrin Speegle)
    Proc. Amer. Math. Soc. 139 (2011), 3247-3256. PDF
  21. Characterization of sequences of frame norms, (with John Jasper)
    J. Reine Angew. Math. 654 (2011), 219-244. PDF
  22. Affine and quasi-affine frames for rational dilation, (with Jakob Lemvig)
    Tran. Amer. Math. Soc. 363 (2011), 1887-1924. PDF
  23. Anisotropic singular integrals in product spaces, (with Baode Li, Dachun Yang, and Yuan Zhou)
    Sci. China Math. 53 (2010), 3163-3178. PDF
  24. Anisotropic classes of homogeneous pseudodifferential symbols, (with Árpád Bényi)
    Studia Math. 200 (2010), 41-66. PDF
  25. 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
  26. Linear independence of Parseval wavelets, (with Darrin Speegle)
    Illinois J. Math. 54 (2010), 771-785. PDF
  27. The closure of the set of tight frame wavelets,
    Acta Appl. Math. 107 (2009), 195-201. PDF
  28. Construction and reconstruction of tight framelets and wavelets via matrix mask functions, (with Ziemowit Rzeszotnik)
    J. Funct. Anal. 256 (2009), 1065-1105. PDF
  29. Intersection of dilates of shift-invariant spaces,
    Proc. Amer. Math. Soc. 137 (2009), 563-572. PDF
  30. Dimension functions of rationally dilated GMRAs and wavelets, (with Kenneth Hoover)
    J. Fourier Anal. Appl. 15 (2009), 585-615. PDF
  31. 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
  32. Baggett's problem for frame wavelets,
    Representations, wavelets, and frames, 153-173, Appl. Numer. Harmon. Anal., Birkhauser Boston, Boston, MA, 2008. PDF
  33. Duality and interpolation of anisotropic Triebel-Lizorkin spaces,
    Math. Z. 259 (2008), 131-169. PDF
  34. Anisotropic Triebel-Lizorkin spaces with doubling measures,
    J. Geom. Anal. 17 (2007), 387-424. PDF
  35. The canonical and alternate duals of a wavelet frame, (with Jakob Lemvig)
    Appl. Comput. Harmon. Anal. 23 (2007), 263-272. PDF
  36. Characterization and perturbation of Gabor frame sequences with rational parameters, (with Ole Christensen)
    J. Approx. Theory 147 (2007), 67-80. PDF
  37. The structure of shift-modulation invariant spaces: the rational case
    J. Funct. Anal. 244 (2007), 172-219. PDF
  38. Connectivity and density in the set of framelets
    Math. Res. Lett. 14 (2007), 285-293. PDF
  39. Duals of Hardy spaces on homogeneous groups (with Gerald B. Folland)
    Math. Nachr. 280 (2007), 1223-1229. PDF
  40. Minimal generator sets for finitely generated shift-invariant subspaces of L2(Rn), (with Norbert Kaiblinger)
    J. Math. Anal. Appl. 313 (2006), 342-352. PDF
  41. The Feichtinger conjecture for wavelet frames, Gabor frames and frames of translates, (with Darrin Speegle)
    Canad. J. Math. 58 (2006), 1121-1143. PDF
  42. Atomic and molecular decompositions of anisotropic Triebel-Lizorkin spaces, (with Kwok-Pun Ho)
    Trans. Amer. Math. Soc. 358 (2006), 1469-1510. PDF
  43. On the existence of multiresolution analysis for framelets (with Ziemowit Rzeszotnik),
    Math. Ann. 332 (2005), 705-720. PDF
  44. Atomic and molecular decompositions of anisotropic Besov spaces,
    Math. Z. 250 (2005), 539-571. PDF
  45. Erratum to: Atomic and Molecular Decompositions of Anisotropic Besov Spaces,
    Math. Z. 273 (2013), 1297-1299. PDF
  46. Boundedness of operators on Hardy spaces via atomic decompositions,
    Proc. Amer. Math. Soc. 133 (2005), 3535-3542. PDF
  47. 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
  48. Biorthogonal wavelets, MRA's and shift-invariant spaces, (with Gustavo Garrigós)
    Studia Math. 160 (2004), 231-248. PDF
  49. Affine Frames, GMRA's, and the Canonical Dual, (with Eric Weber)
    Studia Math. 159 (2003), 453-479. PDF
  50. Riesz wavelets and generalized multiresolution analyses,
    Appl. Comput. Harmon. Anal. 14 (2003), 181-194. PDF
  51. The spectral function of shift-invariant spaces, (with Ziemowit Rzeszotnik)
    Michigan Math. J. 51 (2003), 387-414. PDF
  52. Quasi-affine systems and the Calderòn condition,,
    Harmonic Analysis at Mount Holyoke, Contemp. Math. 320 (2003), 29-43. PDF
  53. Anisotropic Hardy spaces and wavelets,
    Mem. Amer. Math. Soc. 164 (2003), no. 781, 122pp. PDF
  54. On a problem of Daubechies,
    Constr. Approx. 19 (2003), 179-190. PDF
  55. 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
  56. Meyer type wavelet bases in R2, (with Darrin Speegle)
    J. Approx. Theory 116 (2002), 49-75. PDF
  57. Combined MSF multiwavelets,
    J. Fourier Anal. Appl. 8 (2002), 201-210. PDF
  58. The construction of r-regular wavelets for arbitrary dilations,
    J. Fourier Anal. Appl. 7 (2001), 489-506. PDF
  59. On characterizations of multiwavelets in L2(Rn),
    Proc. Amer. Math. Soc. 129 (2001), 3265-3274. PDF
  60. A characterization of dimension functions of wavelets, (with Ziemowit Rzeszotnik and Darrin Speegle)
    Appl. Comput. Harmon. Anal. 10 (2001), 71-92. PDF
  61. Inverse volume inequalities for matrix weights,
    Indiana Univ. Math. J. 50 (2001), 383-410. PDF
  62. The structure of shift invariant subspaces of L2(Rn),
    J. Funct. Anal. 177 (2000), 282-309. PDF
  63. A characterization of affine dual frames in L2(Rn),
    Appl. Comput. Harmon. Anal. 8 (2000), 203-221. PDF
  64. Tight frames of multidimensional wavelets,
    J. Fourier Anal. Appl. 3 (1997), 525-542. PDF