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.

Abstract

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 L2(ℝ) functions. Shannon wavelets are C∞-functions and their any order derivatives can be analytically defined by some kind of a finite hypergeometric series (connection coefficients).