de Branges spaces with bi-Lipschitz phase for large distances

TL;DR

This paper characterizes de Branges spaces with bi-Lipschitz phase for large distances as subspaces of weighted Paley-Wiener spaces, highlighting their structure and integrability properties.

Contribution

It provides a new characterization of de Branges spaces with bi-Lipschitz phase in terms of weighted Paley-Wiener spaces, linking phase properties to weighted integrability.

Findings

De Branges spaces with bi-Lipschitz phase are subspaces of weighted Paley-Wiener spaces.

Elements in these spaces are square-integrable against a heavier weight on the real line.

The characterization connects phase behavior to weighted space structure.

Abstract

We characterize an arbitrary de Branges space with bi-Lipschitz phase for large distances as a subspace of a weighted Paley--Wiener space, consisting of the elements square-integrable against a heavier weight on the real line.