A First Szegő's Limit Theorem for a class of non-Toeplitz matrices

A. Bourget; T. K. McMillen

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arXiv · 1511.06020

A First Szegő's Limit Theorem for a class of non-Toeplitz matrices

A. Bourget·T. K. McMillen

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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 $μ$-distributed for some probability measure. As an application of our results, we extend the well-known class of Kac-Murdock-Szegő generalized Toeplitz matrices to sequences of matrices whose diagonal entries are modeled by Riemann integrable functions.

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BibTeX RIS

A. Bourget, T. K. McMillen. 2015-11-18. A First Szegő's Limit Theorem for a class of non-Toeplitz matrices. https://arxiv.org/abs/1511.06020

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