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Asymptotic distribution of the spectra of a class of generalized Kac–Murdock–Szegö matrices

✍ Scribed by William F. Trench

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
113 KB
Volume
294
Category
Article
ISSN
0024-3795

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✦ Synopsis

We consider symmetric Toeplitz matrices n t jrÀsj n rYs1 with t r aq r baq r , where a and b are real and 0 q 1. We give formulas for det n and À1 n , and show that if a À b 1 and b T 0 then n has eigenvalues k 1n k2n Á Á Á `knn such that lim n3I k 1n ÀI, lim n3I k nn I, and fk 2n Y F F F Y k nÀ1Yn g are equally distributed as n 3 I with values of p h 1 À q 2 1 À 2q cos h q 2 at n À 2 equally spaced points in 0Y p.

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