Oversampling on a class of symmetric regular de Branges spaces

Abstract

A de Branges space is regular if the constants belong to its space of associated functions and is symmetric if it is isometrically invariant under the map . Let be the reproducing kernel in and be the operator of multiplication by the independent variable with maximal domain in . Loosely speaking, we say that has the -oversampling property relative to a proper subspace of it, with , if there exists such that for all , for all and almost every self-adjoint extension of . This definition is motivated by the well-known oversampling property of Paley-Wiener spaces. In this paper, we provide sufficient conditions for a symmetric, regular de Branges space to have the -oversampling property relative to a chain of de Branges subspaces of it.