The eigenvalue distribution of products of Toeplitz matrices - clustering and attraction
Language
en
Article de revue
This item was published in
Linear Algebra and its Applications. 2010-05, vol. 432, n° 10, p. 2658-2678
Elsevier
English Abstract
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, ...Read more >
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.Read less <
Keywords
matrix sequence
joint eigenvalue distribution
Toeplitz matrix
Origin
Hal imported