Exponential bases on two dimensional trapezoids

TL;DR

This paper investigates the existence and stability of exponential Riesz bases on specific two-dimensional trapezoid domains, extending the results to higher dimensions and constructing bases for unions of rectangles.

Contribution

It introduces new exponential bases for L^2 spaces on trapezoids and generalizes the results to higher dimensions, expanding the understanding of basis constructions on complex domains.

Findings

Constructed exponential bases for L^2 on trapezoids composed of rectangles.

Proved stability conditions for these bases.

Extended the theory to higher-dimensional domains.

Abstract

We discuss existence and stability of Riesz bases of exponential type of L^2(T) for special domains T called trapezoids. We construct exponential bases on L^2(T) when T is a finite union of rectangles with the same height. We also generalize our main theorems in dimension d\ge 3.