Article ID Journal Published Year Pages File Type
4605104 Applied and Computational Harmonic Analysis 2014 8 Pages PDF
Abstract

The norm of the commutator of a projection onto a closed subspace and an operator S can be understood as a quantitative measure of the lack of invariance of the space under S  . In this paper we study principal shift-invariant spaces V(φ)V(φ) and their invariance properties under arbitrary translations. It is known that no principal shift-invariant space with an integrable orthonormal basis generator can be fully translation-invariant. In this paper we present several quantitative versions of this statement.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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