Maximal eigenvalue and norm of the product of Toeplitz matrices. Study of a particular case

TL;DR

This paper investigates the asymptotic behavior of the spectral norm of the product of two large Toeplitz matrices generated by functions with Fisher-Hartwig singularities, revealing insights into their eigenvalues as matrix size grows.

Contribution

It provides a detailed analysis of the spectral norm's asymptotics for a specific class of Toeplitz matrix products with Fisher-Hartwig singularities.

Findings

Asymptotic behavior of spectral norm characterized

Eigenvalues of Toeplitz matrix products analyzed

Results applicable to large matrix limits

Abstract

In this paper we describe the asymptotic behaviour of the spectral norm of the product of two finite Toeplitz matrices as the matrix dimension goes to the infinity. These Toeplitz matrices are generated by positive functions with Fisher-Hartwig singularities of negative order. Since we have positive operators it is known that the spectral norm is also the largest eigenvalue of this product.