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arXiv · 1910.05188

Diagonalization of Shift-Preserving Operators

Alejandra Aguilera·Carlos Cabrelli·Diana Carbajal·Victoria Paternostro
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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.

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Alejandra Aguilera, Carlos Cabrelli, Diana Carbajal, Victoria Paternostro. 2019-10-11. Diagonalization of Shift-Preserving Operators. https://arxiv.org/abs/1910.05188

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