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Zbl 1162.42314
Cattani, Carlo
Shannon wavelets theory. (English)
[J] Math. Probl. Eng. 2008, Article ID 164808, 24 p. (2008). ISSN 1024-123X; ISSN 1563-5147/e

Summary: Shannon wavelets are studied together with their differential properties (known as connection coefficients). It is shown that the Shannon sampling theorem can be considered in a more general approach suitable for analyzing functions ranging in multifrequency bands. This generalization coincides with the Shannon wavelet reconstruction of $L_{2}(\Bbb R)$ functions. The differential properties of Shannon wavelets are also studied through the connection coefficients. It is shown that Shannon wavelets are $C^{\infty }$-functions and their any order derivatives can be analytically defined by some kind of a finite hypergeometric series. These coefficients make it possible to define the wavelet reconstruction of the derivatives of the $C^{\ell }$-functions.

MSC 2000:: *42C40 Wavelets

Cited in: Zbl 1221.65332

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Zentralblatt MATH Berlin [Germany]