Weighted Paley-Wiener spaces and mountain chain axioms: a detailed exposition

TL;DR

This paper reviews and generalizes the second half of Lyubarskii and Seip's work on Weighted Paley-Wiener spaces, abstracting axioms for broader de Branges spaces and providing a higher-level theoretical framework.

Contribution

It introduces a more general axiomatic framework for de Branges spaces, extending previous results on Weighted Paley-Wiener spaces.

Findings

Abstracted axioms for a larger class of de Branges spaces

Proved results at a higher level of generality

Enhanced understanding of weighted Paley-Wiener spaces

Abstract

The present work reviews the second half of Lyubarskii and Seip's paper, Weighted Paley--Wiener Spaces. Axioms defining a larger class of de Branges spaces are abstracted, allowing us to state and prove their results at a higher level of generality.