Backward Shift Invariant Subspaces in Reproducing Kernel Hilbert Spaces

TL;DR

This paper characterizes backward shift invariant subspaces within a broad class of reproducing kernel Hilbert spaces, including de Branges-Rovnyak spaces and certain Toeplitz operator range spaces.

Contribution

It provides a comprehensive description of backward shift invariant subspaces for a large class of RKHS, extending previous results to new spaces.

Findings

Characterization of backward shift invariant subspaces in RKHS

Includes de Branges-Rovnyak spaces and Toeplitz operator range spaces

Extends understanding of invariant subspace structure

Abstract

In this note, we describe the backward shift invariant subspaces for a large class of reproducing kernel Hilbert spaces. This class includes in particular de Branges-Rovnyak spaces (the non-extreme case) and the range space of co-analytic Toeplitz operators.