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Mathematical Problems in Engineering
Volume 2010, Article ID 408418, 22 pages
Research Article

Shannon Wavelets for the Solution of Integrodifferential Equations

Department of Pharmaceutical Sciences (diFarma), University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

Received 30 December 2009; Accepted 17 February 2010

Academic Editor: Alexander P. Seyranian

Copyright © 2010 Carlo Cattani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 functions. Shannon wavelets are -functions and their any order derivatives can be analytically defined by some kind of a finite hypergeometric series (connection coefficients).