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