Shannon wavelets are used to define a method for the solution of integrodifferential equations. Thismethod 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 L2R 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.
Shannon Wavelets for the solution of Integro-Differential Equations
CATTANI, Carlo
2010
Abstract
Shannon wavelets are used to define a method for the solution of integrodifferential equations. Thismethod 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 L2R 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
