Systems biorthogonal to exponential systems on a finite union of intervals

TL;DR

This paper investigates the biorthogonal systems to exponential systems in L^2 spaces over finite unions of intervals, demonstrating completeness in specific cases with two or three intervals.

Contribution

It establishes the completeness of biorthogonal systems to exponential systems in L^2 over unions of two or three intervals, extending understanding of their structure.

Findings

Biorthogonal systems are complete for unions of two or three intervals.

The study advances the theory of exponential systems in finite union domains.

Results contribute to spectral theory and functional analysis in non-interval domains.

Abstract

We study the properties of a system biorthogonal to a complete and minimal system of exponentials in $L^2(E)$, where $E$ is a finite union of intervals, and show that in the case when $E$ is a union of two or three intervals the biorthogonal system is also complete.