Diagonalization of Shift-Preserving Operators
Classical Analysis and ODEs
2021-07-06 v2 Functional Analysis
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.
Cite
@article{arxiv.1910.05188,
title = {Diagonalization of Shift-Preserving Operators},
author = {Alejandra Aguilera and Carlos Cabrelli and Diana Carbajal and Victoria Paternostro},
journal= {arXiv preprint arXiv:1910.05188},
year = {2021}
}
Comments
27 pages. To appear in Advances in Mathematics