Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 4, Pages 465-479
doi:10.1155/S1048953398000380

Moment computation in shift invariant spaces

David A. Eubanks,1 Patrick J. van Fleet,2 and Jianzhong Wang2

1Coker College, Department of Mathematics, Hartsville 29550 , SC, USA
2Sam Houston State University, Department of Mathematics, Huntsville 77341, TX, USA

Received 1 December 1996; Revised 1 October 1997

Copyright © 1998 David A. Eubanks et al. 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

An algorithm is given for the computation of moments of f∈S, where S is either a principal h-shift invariant space or S is a finitely generated h-shift invariant space. An error estimate for the rate of convergence of our scheme is also presented. In so doing, we obtain a result for computing inner products in these spaces. As corollaries, we derive Marsden-type identities for principal h-shift invariant spaces and finitely generated h-shift invariant spaces. Applications to wavelet/multiwavelet spaces are presented.