Examples of exponential bases on Union of intervals

TL;DR

This paper constructs explicit exponential bases on unions of intervals and cubes, providing new stability results that generalize Kadec's theorem, with potential applications in harmonic analysis and signal processing.

Contribution

It introduces explicit exponential bases on unions of intervals and cubes, and proves a stability result extending Kadec's -theorem.

Findings

Explicit exponential bases on unions of segments and cubes

Stability results generalizing Kadec's -theorem

Applicable to finite and infinite unions

Abstract

In this paper, we construct explicit exponential bases on finite or infinite unions of segments of total length one with some conditions on gaps between them. We also construct exponential bases on certain unions of cubes in $\R^d$ and we prove a stability result for unions of segments that generalize Kadec's $\frac{1}{4}-$theorem.