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

2012/10/29 by Rambour, Philippe
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1210.7612

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.

Related

• Norms of Toeplitz Matrices with Fisher-Hartwig Symbols
• Spectrum of the product of Toeplitz matrices with application in probability
• Asymptotic eigenvalue distribution of large Toeplitz matrices
• Spectral norm of random Toeplitz matrices
• Expansions for Eigenfunction and Eigenvalues of large-n Toeplitz Matrices