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Asymptotic distribution of the even and odd spectra of real symmetric Toeplitz matrices

✍ Scribed by William F. Trench

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
87 KB
Volume
302-303
Category
Article
ISSN
0024-3795

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✦ Synopsis

If n t rÀs n rYs0 is a real symmetric Toeplitz (RST) matrix then R n has a basis consisting of dna2e eigenvectors x satisfying (A) tx x and na2 eigenvectors y satisfying (B) ty Ày, where t is the ¯ip matrix. We say that an eigenvalue k of n is even if a k-eigenvector of n satis®es (A), or odd if a k-eigenvector of n satis®es (B). We call the collection of even (odd) eigenvalues of n the even (odd) spectrum of n . In the case where t r 1ap p 0 f x cos rx dx a great deal is known about the asymptotic distribution of the eigenvalues of n as n 3 I, under suitable assumptions on f. However, the question of the separate asymptotic distributions of the even and odd spectra does not seem to have been raised.

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