Eigenvalues of Toeplitz matrices in the bulk of the spectrum

TL;DR

This paper investigates the asymptotic behavior of eigenvalues of Toeplitz matrices, confirming a conjecture about their near-periodicity, which advances understanding of spectral properties in mathematical analysis.

Contribution

It proves a conjecture on the near-periodicity of Toeplitz eigenvalues, providing new insights into their spectral asymptotics.

Findings

Eigenvalues exhibit near-periodicity as matrix size grows

Confirmed conjecture of Levitin and Shargorodsky

Enhanced understanding of Toeplitz spectral asymptotics

Abstract

The authors analyze the asymptotics of eigenvalues of Toeplitz matrices with certain continuous and discontinuous symbols. In particular, the authors prove a conjecture of Levitin and Shargorodsky on the near-periodicity of Toeplitz eigenvalues.