Spectral properties of Jacobi matrices by asymptotic analysis

Authors:
Jan Janas;Marcin Moszyński
Affiliations:
Instytut Matematyczny Polskiej Akademii Nauk, ul. św. Tomasza 30, 31-027 Kraków, Poland;Wydzial Matematyki Informatyki i Mechaniki, Uniwersytet Warszawski, ul. Banacha 2, 02-097 Warszawa, Poland
Venue:
Journal of Approximation Theory
Year:
2003

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Abstract

We consider two classes of Jacobi matrix operators in l2 with zero diagonals and with weights of the form nα + cn for 0 nα + cnnα-1 for α 1, where {cn} is periodic. We study spectral properties of these operators (especially for even periods), and we find asymptotics of some of their generalized eigensolutions. This analysis is based on some discrete versions of the Levinson theorem, which are also proved in the paper and may be of independent interest.