Title

Pointwise Convergence Of A Class Of Non-Orthogonal Wavelet Expansions

Keywords

Non-orthogonal wavelets; Pointwise convergence; Shannon's wavelet; Wavelet expansions

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. © 2000 American Mathematical Society.

Publication Date

1-1-2000

Publication Title

Proceedings of the American Mathematical Society

Volume

128

Issue

12

Number of Pages

3629-3637

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/s0002-9939-00-05506-4

Socpus ID

33746008517 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/33746008517

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