Exponential bases on modified domains

TL;DR

This paper investigates the stability of exponential bases on measurable domains in the real line when the domains undergo small modifications, expanding understanding beyond phase perturbations.

Contribution

It introduces a new analysis of exponential bases on measurable domains and examines their stability under small domain modifications.

Findings

Exponential bases remain stable under certain small domain modifications.

The study extends stability results beyond phase perturbations.

Provides conditions for stability of exponential bases on measurable domains.

Abstract

The stability of exponential bases on domains in $\R^n$ has been widely studied, with much of the research focusing on small perturbations of the phase. In this paper, we consider bases on measurable domains of the real line, and their stability under small modifications of the domain is investigated.