Integrability of the continuum wavelet kernel
HTML articles powered by AMS MathViewer
- by Mark A. Pinsky PDF
- Proc. Amer. Math. Soc. 132 (2004), 1729-1737 Request permission
Abstract:
We state and prove sufficient conditions for the absolute integrability of the inverse of the continuum wavelet kernel.References
- 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, DOI 10.1137/0515056
- A.-P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113–190. MR 167830, DOI 10.4064/sm-24-2-113-190
- 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, DOI 10.1137/1.9781611970104
- 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, DOI 10.1090/cbms/079
- 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, DOI 10.1201/9781420049985
- J. P. Kahane and P. G. LeMarie Rieusset, Fourier Series and Wavelets, Gordon and Breach, Amsterdam, 1995.
- 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, DOI 10.1090/mmono/177
- Stéphane Mallat, A wavelet tour of signal processing, Academic Press, Inc., San Diego, CA, 1998. MR 1614527
- Sadahiro Saeki, On the reproducing formula of Calderón, J. Fourier Anal. Appl. 2 (1995), no. 1, 15–28. MR 1361540, DOI 10.1007/s00041-001-4020-9
- Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
Additional Information
- Mark A. Pinsky
- Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2730
- Email: pinsky@math.nwu.edu
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1729-1737
- MSC (2000): Primary 42C40; Secondary 44A35
- DOI: https://doi.org/10.1090/S0002-9939-03-07253-8
- MathSciNet review: 2051134