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

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.