SERRA-CAPIZZANO, Stefano; SESANA, Debora; STROUSE, Elizabeth

doi:10.1016/j.laa.2009.12.005

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SERRA-CAPIZZANO, Stefano
Department of Physics and Mathematics

SESANA, Debora
Department of Physics and Mathematics

STROUSE, Elizabeth
Institut de Mathématiques de Bordeaux [IMB]

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Linear Algebra and its Applications. 2010-05, vol. 432, n° 10, p. 2658-2678

Elsevier

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We use a recent result concerning the eigenvalues of a generic (non Hermitian) complex perturbation of a bounded Hermitian sequence of matrices to prove that the asymptotic spectrum of the product of Toeplitz sequences, whose symbols have a real-valued essen- tially bounded product h, is described by the function h in the "Szeg ̈ way". Then, using Mergelyan's theorem, we extend the result to the more general case where h belongs to the Tilli class. The same technique gives us the analogous result for sequences belonging to the algebra generated by Toeplitz sequences, if the symbols associated with the sequences are bounded and the global symbol h belongs to the Tilli class. A generalization to the case of multilevel matrix-valued symbols and a study of the case of Laurent polynomials not necessarily belonging to the Tilli class are also given.< Leer menos

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matrix sequence

joint eigenvalue distribution

Toeplitz matrix

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The eigenvalue distribution of products of Toeplitz matrices - clustering and attraction

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