A First Szeg\H{o}'s Limit Theorem for a class of non-Toeplitz matrices
Spectral Theory
2015-11-20 v1
Abstract
We compute the limiting statistical distribution of the eigenvalues of sequences of matrices whose entries satisfy what we call a vanishing mean variation condition and are -distributed for some probability measure. As an application of our results, we extend the well-known class of Kac-Murdock-Szeg\H{o} generalized Toeplitz matrices to sequences of matrices whose diagonal entries are modeled by Riemann integrable functions.
Keywords
Cite
@article{arxiv.1511.06020,
title = {A First Szeg\H{o}'s Limit Theorem for a class of non-Toeplitz matrices},
author = {A. Bourget and T. K. McMillen},
journal= {arXiv preprint arXiv:1511.06020},
year = {2015}
}