An equilibrium problem for the limiting eigenvalue distribution of rational Toeplitz matrices

Details An equilibrium problem for the limiting eigenvalue distribution of rational Toeplitz matrices An equilibrium problem for the limiting eigenvalue distribution of rational Toeplitz matrices

2009-11-25

arxiv.org/abs/0911.4897v1

Mathematics

Complex Variables

20 pages, 2 figures

Scientific paper

We consider the asymptotic behavior of the eigenvalues of Toeplitz matrices with rational symbol as the size of the matrix goes to infinity. Our main result is that the weak limit of the normalized eigenvalue counting measure is a particular component of the unique solution to a vector equilibrium problem. Moreover, we show that the other components describe the limiting behavior of certain generalized eigenvalues. In this way, we generalize the recent results of Duits and Kuijlaars for banded Toeplitz matrices.

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