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Wavelet decompositions of Fourier multipliers
Authors:
Earl Berkson, Maciej Paluszynski and Guido Weiss
Journal:
Proc. Amer. Math. Soc. 125 (1997), 2395-2399
MSC (1991):
Primary 42A45, 42C15
MathSciNet review:
1416076
Full-text PDF Free Access
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Abstract: We show that in terms of its weak topology, the space of Fourier multipliers for  ,  , can be decomposed by band-limited wavelets belonging to the Schwartz class.
- 1.
Nakhlé
Asmar, Earl
Berkson, and T.
A. Gillespie, On Jodeit’s multiplier extension theorems,
J. Anal. Math. 64 (1994), 337–345. MR 1303518
(96j:42001), http://dx.doi.org/10.1007/BF03008415
- 2.
Pascal
Auscher, Solution of two problems on wavelets, J. Geom. Anal.
5 (1995), no. 2, 181–236. MR 1341029
(96g:42016), http://dx.doi.org/10.1007/BF02921675
- 3.
Pascal
Auscher, Guido
Weiss, and M.
Victor Wickerhauser, Local sine and cosine bases of Coifman and
Meyer and the construction of smooth wavelets, Wavelets, Wavelet
Anal. Appl., vol. 2, Academic Press, Boston, MA, 1992,
pp. 237–256. MR 1161254
(93e:42042)
- 4.
Aline
Bonami, Fernando
Soria, and Guido
Weiss, Band-limited wavelets, J. Geom. Anal.
3 (1993), no. 6, 543–578. MR 1248085
(94k:42046), http://dx.doi.org/10.1007/BF02921322
- 5.
Alessandro
Figà-Talamanca, Translation invariant operators in
𝐿^{𝑝}, Duke Math. J. 32 (1965),
495–501. MR 0181869
(31 #6095)
- 6.
P.G. Lemarié and Y. Meyer, Ondelettes et bases hilbertiennes, Rev. Mat. Iberoamericana 2 (1986), 1-18. CMP 19:04
- 7.
Yves
Meyer, Ondelettes et algorithmes concurrents,
Actualités Scientifiques et Industrielles [Current Scientific and
Industrial Topics], vol. 1435, Hermann, Paris, 1992 (French, with
French summary). MR 1204654
(94g:42059)
- 1.
- N. Asmar, E. Berkson, and T.A. Gillespie, On Jodeit's multiplier extension theorems, Journal d'Analyse Math. 64 (1994), 337-345. MR 96j:42001
- 2.
- P. Auscher, Solution of two problems on wavelets,, J. Geometric Analysis 5 (1995), 181-236. MR 96g:42016
- 3.
- P. Auscher, G. Weiss, and M.V. Wickerhauser, Local sine and cosine bases of Coifman and Meyer and the construction of smooth wavelets, ``Wavelets: A Tutorial in Theory and Applications'', Academic Press, New York, 1992, pp. 237-256. MR 93e:42042
- 4.
- A. Bonami, F. Soria, and G. Weiss, Band limited wavelets, J. Geometric Analysis 3 (1993), 543-578. MR 94k:42046
- 5.
- A. Figà-Talamanca, Translation invariant operators in
 , Duke Math. J. 32 (1965), 495-501. MR 31:6095
- 6.
- P.G. Lemarié and Y. Meyer, Ondelettes et bases hilbertiennes, Rev. Mat. Iberoamericana 2 (1986), 1-18. CMP 19:04
- 7.
- Y. Meyer, Ondelettes et algorithmes concurrents, Actualités Scientifiques et Industrielles 1435,
Hermann, Paris, 1992. MR 94g:42059
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Additional Information
Earl Berkson
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green St., Urbana, Illinois 61801
Maciej Paluszynski
Affiliation:
Institute of Mathematics, University of Wroclaw, Wroclaw, Poland
Guido Weiss
Affiliation:
Department of Mathematics, Washington University, St. Louis, Missouri 63130
DOI:
http://dx.doi.org/10.1090/S0002-9939-97-03991-9
PII:
S 0002-9939(97)03991-9
Received by editor(s):
March 4, 1996
Additional Notes:
The work of the first and third authors was supported by separate grants from the National Science Foundation (U.S.A.)
The second author wishes to thank DARPA for its support
Communicated by:
J. Marshall Ash
Article copyright:
© Copyright 1997 American Mathematical Society
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