This article is cited in 3 papers

On Compact Perturbations of the Limit-Periodic Jacobi Operator

V. A. Kalyagin^a, A. A. Kononova<sup>b

a</sup> State University – Higher School of Economics, Nizhny Novgorod Branch
^b Nizhny Novgorod State Technical University

Abstract: We consider a bounded Jacobi operator acting in the space $l^2(\mathbb N)$. We supplement the spectral measure of this operator by a set of finitely many discrete masses (on the real axis outside the convex hull of the support of the operator's spectral measure). In the present paper, we study whether the obtained perturbation of the original operator is compact. For limit-periodic Jacobi operators, we obtain a necessary and sufficient condition on the location of the masses for the perturbation to be compact.

Keywords: compact perturbations, Jacobi operator, spectral measure, discrete masses, the space $\ell^2(\mathbb N)$, finite-zone operator, harmonic function.

UDC: 517.984

Received: 05.12.2008

DOI: 10.4213/mzm6624

 English version: Mathematical Notes, 2009, 86:6, 789–800

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