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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Pointwise convergence of a class of non-orthogonal wavelet expansions

Author: Ahmed I. Zayed
Journal: Proc. Amer. Math. Soc. 128 (2000), 3629-3637
MSC (1991): Primary 42C15, 42C05; Secondary 40A05, 40A30
Published electronically: June 7, 2000
MathSciNet review: 1695334
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Abstract: Non-orthogonal wavelet expansions associated with a class of mother wavelets is considered. This class of wavelets comprises mother wavelets that are not necessarily integrable over the whole real line, such as Shannon's wavelet. The pointwise convergence of these wavelet expansions is investigated. It is shown that, unlike other wavelet expansions, the ones under consideration do not necessarily converge pointwise to the functions at points of continuity, unless a more stringent condition, such as bounded variation, is imposed.

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Additional Information

Ahmed I. Zayed
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816

PII: S 0002-9939(00)05506-4
Keywords: Non-orthogonal wavelets, Shannon's wavelet, wavelet expansions, pointwise convergence
Received by editor(s): June 16, 1998
Received by editor(s) in revised form: February 24, 1999
Published electronically: June 7, 2000
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2000 American Mathematical Society

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