http://dx.doi.org/10.1006/jmaa.1994.1150

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Title

Wavelet Transform Of Periodic Generalized-Functions

Authors

Authors

A. I. Zayed

Comments

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Abbreviated Journal Title

J. Math. Anal. Appl.

Keywords

ATOMIC DECOMPOSITIONS; SAMPLING THEORY; BANACH-SPACES; HARDY-SPACES; SIGNAL; PROPAGATION; Mathematics, Applied; Mathematics

Abstract

The aim of this paper is to define the wavelet transform for spaces of periodic functions, then extend this definition to spaces of generalized functions larger than the space of periodic Schwartz distributions, such as spaces of periodic Beurling ultradistributions and hyperfunctions on the unit circle. It is shown that the wavelet transforms of such generalized functions are nice and smooth functions defined on an infinite cylinder, provided that the analyzing wavelet is also nice and smooth. For example, it is shown that the growth rate of the derivatives of the wavelet transform is almost as good as that of the analyzing wavelet. More precisely, if the mother wavelet g satisfies Sup(x is-an-element-of R)\x(g)g(q)(x)\ less-than-or-equal-to CA(k)B(q)k(kbeta)q(qalpha) (k, q = 0, 1, 2, ...), then the wavelet transform W(g)(f) of a periodic Beurling ultradistribution f satisfies sup(r,theta) is-an-element-of Y epsilon\r(k) partial derivative(theta)p partial derivative(r)q)W(g)(f)(r, theta)\ less-than-or-equal-to DA(k)k(alphak)B(p)C(q)p(palpha)q(q)(alpha + beta); k, p, q greater-than-or-equal-to 0, where Y(epsilon) = {(r, theta): r greater-than-or-equal-to epsilon > 0, theta is-an-element-of T}. (C) 1994 Academic Press, Inc.

Journal Title

Journal of Mathematical Analysis and Applications

Volume

183

Issue/Number

2

Publication Date

1-1-1995

Document Type

Article

Language

English

First Page

391

Last Page

412

WOS Identifier

WOS:A1994NN53500006

ISSN

0022-247X

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