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Zbl 1191.65174
Cattani, Carlo
Shannon wavelets for the solution of integrodifferential equations.
(English)
[J] Math. Probl. Eng. 2010, Article ID 408418, 22 p. (2010). ISSN 1024-123X; ISSN 1563-5147/e

Summary: Shannon wavelets are used to define a method for the solution of integrodifferential equations. This method is based on (1) the Galerking method, (2) the Shannon wavelet representation, (3) the decorrelation of the generalized Shannon sampling theorem, and (4) the definition of connection coefficients. The Shannon sampling theorem is considered in a more general approach suitable for analysing functions ranging in multifrequency bands. This generalization coincides with the Shannon wavelet reconstruction of $L_{2}(\Bbb R)$ functions. Shannon wavelets are $C^{\infty }$-functions and their any order derivatives can be analytically defined by some kind of a finite hypergeometric series (connection coefficients).
MSC 2000:
*65R20 Integral equations (numerical methods)
45B05 Fredholm integral equations
65T60 Wavelets

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