DIAGONALIZATION OF SHIFT-PRESERVING OPERATORS

AGUILERA, A.,; CABRELLI, C.; CARBAJAL, D.; PATERNOSTRO, V.

ADVANCES IN MATHEMATICS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2021

0001-8708

In this note we study the structure of shift-preserving operators act- ing on a finitely generated shift-invariant space. We define a new notion of diago- nalization 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 op- erators.