#### Title

Wavelet Transform Of Periodic Generalized-Functions

#### 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

#### ISSN

0022-247X

#### Recommended Citation

"Wavelet Transform Of Periodic Generalized-Functions" (1995). *Faculty Bibliography 1990s*. 1253.

https://stars.library.ucf.edu/facultybib1990/1253

## Comments

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