The infimum cosine angle between two finitely generated shift-invariant spaces and its applications

Abstract

An expression of the infimum cosine angle between two finite dimensional subspaces is given in terms of Gramians and is applied to find a useful formula for the infimum cosine angle between two finitely generated shift-invariant subspaces of L-2(R-d) in terms of the generators. We then present new equivalent conditions for the existence of the oblique projection between two finitely generated shift-invariant subspaces, thereby providing a constructive method to generate oblique dual frames. This result is a generalization of a result of Aldroubi and is closely related with the biorthogonality of two frame multiresolution analyses. Finally, we illustrate our results by examples. (c) 2005 Elsevier Inc. All rights reserved.