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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
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Abstract: We show that in terms of its weak${}^{*}$ topology, the space of Fourier multipliers for $L^{p}(\mathbb {R})$, $1<p<\infty $, can be decomposed by band-limited wavelets belonging to the Schwartz class.

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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

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