Combining Riesz bases in $R^d$

TL;DR

This paper proves that any finite union of rectangles in multi-dimensional space admits a Riesz basis of exponential functions, expanding the understanding of basis constructions in harmonic analysis.

Contribution

It introduces a method to construct Riesz bases of exponentials for finite unions of rectangles in R^d, a new result in basis theory.

Findings

Finite unions of rectangles in R^d admit Riesz bases of exponentials.

The construction extends basis theory to more complex geometric sets.

Results have implications for harmonic analysis and signal processing.

Abstract

We prove that every finite union of rectangles in $R^d$ admits a Riesz basis of exponentials.