Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Integrability of the continuum wavelet kernel

Author: Mark A. Pinsky
Journal: Proc. Amer. Math. Soc. 132 (2004), 1729-1737
MSC (2000): Primary 42C40; Secondary 44A35
Published electronically: October 15, 2003
MathSciNet review: 2051134
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We state and prove sufficient conditions for the absolute integrability of the inverse of the continuum wavelet kernel.

References [Enhancements On Off] (What's this?)

  • [GM] A. Grossmann and J. Morlet, Decomposition of Hardy functions into square integrable wavelets of constant shape, SIAM J. Math. Anal. 15 (1984), no. 4, 723–736. MR 747432, 10.1137/0515056
  • [C] A.-P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113–190. MR 0167830
  • [D] Ingrid Daubechies, Ten lectures on wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 61, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992. MR 1162107
  • [FJW] Michael Frazier, Björn Jawerth, and Guido Weiss, Littlewood-Paley theory and the study of function spaces, CBMS Regional Conference Series in Mathematics, vol. 79, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1991. MR 1107300
  • [HW] Eugenio Hernández and Guido Weiss, A first course on wavelets, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1996. With a foreword by Yves Meyer. MR 1408902
  • [KL] J. P. Kahane and P. G. LeMarie Rieusset, Fourier Series and Wavelets, Gordon and Breach, Amsterdam, 1995.
  • [I] Satoru Igari, Real analysis—with an introduction to wavelet theory, Translations of Mathematical Monographs, vol. 177, American Mathematical Society, Providence, RI, 1998. Translated from the 1996 Japanese original by the author. MR 1640687
  • [M] Stéphane Mallat, A wavelet tour of signal processing, Academic Press, Inc., San Diego, CA, 1998. MR 1614527
  • [S] Sadahiro Saeki, On the reproducing formula of Calderón, J. Fourier Anal. Appl. 2 (1995), no. 1, 15–28. MR 1361540, 10.1007/s00041-001-4020-9
  • [SW] Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, N.J., 1971. Princeton Mathematical Series, No. 32. MR 0304972

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 42C40, 44A35

Retrieve articles in all journals with MSC (2000): 42C40, 44A35

Additional Information

Mark A. Pinsky
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2730

Received by editor(s): June 23, 2002
Received by editor(s) in revised form: January 29, 2003
Published electronically: October 15, 2003
Communicated by: Andreas Seeger
Article copyright: © Copyright 2003 American Mathematical Society