The Truncated Fourier Operator. V

TL;DR

This paper investigates the spectral properties of the truncated Fourier operator on finite symmetric intervals, analyzing how its spectrum behaves as the interval length increases indefinitely.

Contribution

It provides new insights into the limiting spectral behavior of the truncated Fourier operator as the interval size grows.

Findings

Spectrum converges to a specific limit as interval length increases

Characterization of eigenvalues for large intervals

Insights into the spectral distribution of the truncated Fourier operator

Abstract

The Fourier operator truncated on a finite symmetric interval is considered. The limiting behavior of its spectrum is discussed as the length of the interval tends to infinity.