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The paper is concerned with finite Hermitian Toeplitz matrices whose entries in the first row grow like a polynomial. Such matrices cannot be viewed as truncations of an infinite Toeplitz matrix which is generated by an integrable function or a nice measure. The main results describe the first-order asymptotics of the extreme eigenvalues as the matrix… (More)

We study the asymptotic behavior of individual eigenvalues of the n × n truncations of certain infinite Hessenberg Toeplitz matrices as n goes to infinity. The generating function of the Toeplitz matrices is supposed to be of the form a(t) = t −1 (1−t) α f (t) (t ∈ T), where α is a positive real number but not an integer and f is a smooth function in H ∞.… (More)

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