Asymptotics of individual eigenvalues of a class of large Hessenberg Toeplitz matrices
نویسندگان
چکیده
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)αf(t) (t ∈ T), where α is a positive real number but not an integer and f is a smooth function in H∞. The classes of generating functions considered here and in a recent paper by Dai, Geary, and Kadanoff are overlapping, and in the overlapping cases, our results imply in particular a rigorous justification of an asymptotic formula which was conjectured by Dai, Geary, and Kadanoff on the basis of numerical computations. MSC 2010. Primary 47B35. Secondary 15A15, 15A18, 47N50, 65F15
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