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The limit of the spectral radius of nonnegative Toeplitz matrices (1998)
BibTeX
@MISC{Elsner98thelimit,
author = {Ludwig Elsner and S. Friedland},
title = {The limit of the spectral radius of nonnegative Toeplitz matrices},
year = {1998}
}
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Abstract
A bi-infinite sequence :::t \Gamma2 ; t \Gamma1 ; t 0 ; t 1 ; t 2 ; ::: of nonnegative numbers defines a sequence of nonnegative Toeplitz matrices T n = (t ik ); n = 1; :::;, where t ik = t k\Gammai ; i; k = 1; : : : ; n. We show that the limit of the spectral radius of T n , as n tends to infinity, is given by inffoe(¸) : ¸ 2 [0; 1]g, where oe(¸) = P j2Z t j ¸ j . A corresponding result holds in the case of block Toeplitz matrices, where the t i are p \Theta p\Gammanonnegative matrices and oe(¸) is the spectral radius of P j2Z ¸ j t j . 1 1 Introduction Let t = ft i g i2Z be a bi-infinite sequence of complex numbers. It defines a sequence of Toeplitz matrices T n = (t ik ); n = 1; 2; : : :, where t ik = t k\Gammai ; i; k = 1; : : : ; n. In the case that t \Gammai = ¯ t i ; i 2 Z, i.e. each T n is a hermitian matrix, the asymptotic distribution of the Supported by SFB 343 "Diskrete Strukturen in der Mathematik", Universitat Bielefeld 1 1991 Mathematics Subject Classif...
Keyphrases
spectral radius nonnegative toeplitz matrix ik gammai bi-infinite sequence nonnegative number der mathematik universitat bielefeld theta gammanonnegative matrix diskrete strukturen block toeplitz matrix hermitian matrix introduction let corresponding result complex number toeplitz matrix mathematics subject classif asymptotic distribution
