Diagonalization of Shift-Preserving Operators

2019/10/11 by Aguilera, Alejandra, Cabrelli, Carlos, Carbajal, Diana +1 · 1 citation
#42C15 #47A05 #47A15 #94A20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1910.05188

Abstract

In this note we study the structure of shift-preserving operators acting on a finitely generated shift-invariant space. We define a new notion of diagonalization for these operators, which we call s-diagonalization. We give necessary and sufficient conditions on a bounded shift-preserving operator in order to be s-diagonalizable. These conditions are in terms of its range operator. We also obtain a generalized Spectral Theorem for normal bounded shift-preserving operators.

Cited by

• Convolution and product in finitely generated shift-invariant spaces

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