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 mbownik@uoregon.edu if you would like to receive a reprint.

  1. Extension of shift-invariant systems in L2(R) to frames, (with Ole Christensen, Xinli Huang, and Baiyun Yu)
    Numer. Funct. Anal. Optim. (to appear) PDF
  2. Fourier transform of anisotropic Hardy spaces, (with Li-An Daniel Wang)
    Proc. Amer. Math. Soc. (to appear). PDF
  3. Extrapolation of discrete Triebel-Lizorkin spaces,
    Math. Nachr. (to appear). PDF
  4. Anisotropic classes of inhomogeneous pseudodifferential symbols, (with Árpád Bényi)
    Collect. Math. (to appear). PDF
  5. Oversampling of wavelet frames for real dilations, (with Jakob Lemvig)
    J. London Math. Soc. (to appear). PDF
  6. Duality of weighted anisotropic Besov and Triebel-Lizorkin spaces, (with Baode Li, Dachun Yang, and Wen Yuan)
    Positivity (to appear). PDF
  7. Orthonormal dilations of non-tight frames, (with John Jasper and Darrin Speegle)
    Proc. Amer. Math. Soc. 139 (2011), 3247-3256. PDF
  8. Characterization of sequences of frame norms, (with John Jasper)
    J. Reine Angew. Math. 654 (2011), 219-244. PDF
  9. Affine and quasi-affine frames for rational dilation, (with Jakob Lemvig)
    Tran. Amer. Math. Soc. 363 (2011), 1887-1924. PDF
  10. Anisotropic singular integrals in product spaces, (with Baode Li, Dachun Yang, and Yuan Zhou)
    Sci. China Math. 53 (2010), 3163-3178. PDF
  11. Anisotropic classes of homogeneous pseudodifferential symbols, (with Árpád Bényi)
    Studia Math. 200 (2010), 41-66. PDF
  12. 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
  13. Linear independence of Parseval wavelets, (with Darrin Speegle)
    Illinois J. Math. 54 (2010), 771-785. PDF
  14. The closure of the set of tight frame wavelets,
    Acta Appl. Math. 107 (2009), 195-201. PDF
  15. Construction and reconstruction of tight framelets and wavelets via matrix mask functions, (with Ziemowit Rzeszotnik)
    J. Funct. Anal. 256 (2009), 1065-1105. PDF
  16. Intersection of dilates of shift-invariant spaces,
    Proc. Amer. Math. Soc. 137 (2009), 563-572. PDF
  17. Dimension functions of rationally dilated GMRAs and wavelets, (with Kenneth Hoover)
    J. Fourier Anal. Appl. 15 (2009), 585-615. PDF
  18. 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
  19. Baggett's problem for frame wavelets,
    Representations, Wavelets and Frames: A Celebration of the Mathematical Work of Lawrence Baggett, 153-173, Birkhauser, 2008. PDF
  20. Duality and interpolation of anisotropic Triebel-Lizorkin spaces,
    Math. Z. 259 (2008), 131-169. PDF
  21. Anisotropic Triebel-Lizorkin spaces with doubling measures,
    J. Geom. Anal. 17 (2007), 387-424. PDF
  22. The canonical and alternate duals of a wavelet frame, (with Jakob Lemvig)
    Appl. Comput. Harmon. Anal. 23 (2007), 263-272. PDF
  23. Characterization and perturbation of Gabor frame sequences with rational parameters, (with Ole Christensen)
    J. Approx. Theory 147 (2007), 67-80. PDF
  24. The structure of shift-modulation invariant spaces: the rational case
    J. Funct. Anal. 244 (2007), 172-219. PDF
  25. Connectivity and density in the set of framelets
    Math. Res. Lett. 14 (2007), 285-293. PDF
  26. Duals of Hardy spaces on homogeneous groups (with Gerald B. Folland)
    Math. Nachr. 280 (2007), 1223-1229. PDF
  27. Minimal generator sets for finitely generated shift-invariant subspaces of L2(Rn), (with Norbert Kaiblinger)
    J. Math. Anal. Appl. 313 (2006), 342-352. PDF
  28. The Feichtinger conjecture for wavelet frames, Gabor frames and frames of translates, (with Darrin Speegle)
    Canad. J. Math. 58 (2006), 1121-1143. PDF
  29. Atomic and molecular decompositions of anisotropic Triebel-Lizorkin spaces, (with Kwok-Pun Ho)
    Trans. Amer. Math. Soc. 358 (2006), 1469-1510. PDF
  30. On the existence of multiresolution analysis for framelets (with Ziemowit Rzeszotnik),
    Math. Ann. 332 (2005), 705-720. PDF
  31. Atomic and molecular decompositions of anisotropic Besov spaces,
    Math. Z. 250 (2005), 539-571. PDF
  32. Boundedness of operators on Hardy spaces via atomic decompositions,
    Proc. Amer. Math. Soc. 133 (2005), 3535-3542. PDF
  33. 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
  34. Biorthogonal wavelets, MRA's and shift-invariant spaces, (with Gustavo Garrigós)
    Studia Math. 160 (2004), 231-248. PDF
  35. Affine Frames, GMRA's, and the Canonical Dual, (with Eric Weber)
    Studia Math. 159 (2003), 453-479. PDF
  36. Riesz wavelets and generalized multiresolution analyses,
    Appl. Comput. Harmon. Anal. 14 (2003), 181-194. PDF
  37. The spectral function of shift-invariant spaces, (with Ziemowit Rzeszotnik)
    Michigan Math. J. 51 (2003), 387-414. PDF
  38. Quasi-affine systems and the Calderòn condition,,
    Harmonic Analysis at Mount Holyoke, Contemp. Math. 320 (2003), 29-43. PDF
  39. Anisotropic Hardy spaces and wavelets,
    Mem. Amer. Math. Soc. 164 (2003), no. 781, 122pp. PDF
  40. 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
  41. On a problem of Daubechies,
    Constr. Approx. 19 (2003), 179-190. PDF
  42. Meyer type wavelet bases in R2, (with Darrin Speegle)
    J. Approx. Theory 116 (2002), 49-75. PDF
  43. Combined MSF multiwavelets,
    J. Fourier Anal. Appl. 8 (2002), 201-210. PDF
  44. The construction of r-regular wavelets for arbitrary dilations,
    J. Fourier Anal. Appl. 7 (2001), 489-506. PDF
  45. On characterizations of multiwavelets in L2(Rn),
    Proc. Amer. Math. Soc. 129 (2001), 3265-3274. PDF
  46. A characterization of dimension functions of wavelets, (with Ziemowit Rzeszotnik and Darrin Speegle)
    Appl. Comput. Harmon. Anal. 10 (2001), 71-92. PDF
  47. Inverse volume inequalities for matrix weights,
    Indiana Univ. Math. J. 50 (2001), 383-410. PDF
  48. The structure of shift invariant subspaces of L2(Rn),
    J. Funct. Anal. 177 (2000), 282-309. PDF
  49. A characterization of affine dual frames in L2(Rn),
    Appl. Comput. Harmon. Anal. 8 (2000), 203-221. PDF
  50. Tight frames of multidimensional wavelets,
    J. Fourier Anal. Appl. 3 (1997), 525-542. PDF

Last updated: December 29, 2011.