Exponential bases on multi-rectangles in $\mathbb{R}^d$

TL;DR

This paper constructs explicit exponential bases on finite unions of disjoint rectangles in  with rational vertices, expanding the understanding of basis functions in multi-dimensional spaces.

Contribution

It introduces a method to explicitly build exponential bases on unions of rectangles with rational vertices in , a novel contribution to basis construction in harmonic analysis.

Findings

Explicit exponential bases are constructed for unions of rectangles with rational vertices.

The bases are applicable in  spaces, broadening the scope of basis functions in harmonic analysis.

The method provides a new tool for analyzing functions on complex geometric domains.

Abstract

We construct explicit exponential bases on finite unions of disjoint rectangles of $\mathbb{R}^d$ with rational vertices.