Currently displaying 1 – 3 of 3

Showing per page

Order by Relevance | Title | Year of publication

Slowly oscillating perturbations of periodic Jacobi operators in l²(ℕ)

Marcin Moszyński — 2009

Studia Mathematica

We prove that the absolutely continuous part of the periodic Jacobi operator does not change (modulo unitary equivalence) under additive perturbations by compact Jacobi operators with weights and diagonals defined in terms of the Stolz classes of slowly oscillating sequences. This result substantially generalizes many previous results, e.g., the one which can be obtained directly by the abstract trace class perturbation theorem of Kato-Rosenblum. It also generalizes several results concerning perturbations...

Spectral analysis of unbounded Jacobi operators with oscillating entries

Jan Janas;  Marcin Moszyński — 2012

Studia Mathematica

We describe the spectra of Jacobi operators J with some irregular entries. We divide ℝ into three “spectral regions” for J and using the subordinacy method and asymptotic methods based on some particular discrete versions of Levinson’s theorem we prove the absolute continuity in the first region and the pure pointness in the second. In the third region no information is given by the above methods, and we call it the “uncertainty region”. As an illustration, we introduce and analyse the OP family...

Page 1

Download Results (CSV)