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Asymptotics of the eigenvalues of Toeplitz forms

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Abstract

In this paper we obtain a refinement of Szegö's well-known theorem on the asymptotics of the eigenvalues of Toeplitz forms.

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Literature cited

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    O. Toeplitz, “Theorie der L-Formen,” Math. Ann.,70, 351–376 (1911).

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    U. Grenander and G. Szegö, Toeplitz Forms and Their Applications, University of California Press, Berkeley and Los Angeles (1958).

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    M. Kac, “Toeplitz matrices, translation kernels, and a related problem in probability theory,” Duke Math. J.,21, 501–509 (1954).

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    G. Szegö, “On certain hermitian forms associated with the Fourier series of a positive function,” Communications du Seminaire mathématique de l'université de Lund, tome supplémentaire dédie a′ Marcel Riesz (1952), pp. 228–238.

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    I. A. Ibragimov, “On a theorem of G. Szegö,” Matem. Zametki,3, No. 6, 693–702 (1968).

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Additional information

Translated from Matematicheskie Zametki, Vol. 11, No. 2, pp. 151–158, February, 1972.

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Libkind, L.M. Asymptotics of the eigenvalues of Toeplitz forms. Mathematical Notes of the Academy of Sciences of the USSR 11, 97–101 (1972). https://doi.org/10.1007/BF01097924

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Keywords

  • Toeplitz Form