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 Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 369–405 (Mi semr1064)

Real, complex and functional analysis

The matrix analysis of spectral projections for the perturbed self-adjoint operators

N. B. Uskova

Voronezh State Technical University, 14, Moskovsky ave., Voronezh, 394026, Russia

Abstract: We study bounded perturbations of an unbounded positive definite self-adjoint operator with discrete spectrum. The spectrum has semi-simple eigenvalues with finite geometric multiplicity and the perturbation belongs to operator space defined by rate of the off-diagonal decay of the operator matrix. We show that the spectral projections and the resolvent of the perturbed operator belong to the same space as the perturbation. These results are applied to the Hill operator and the operator with matrix potential. We also consider the inverse problem and the modified Galerkin method.

Keywords: the method of similar operators, the Hill operator, spectral projection.

 Funding Agency Grant Number Russian Foundation for Basic Research 19-01-0073216-01-00197_à

DOI: https://doi.org/10.33048/semi.2019.16.022

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Bibliographic databases:

UDC: 517.9
MSC: 35L75
Received November 28, 2017, published March 19, 2019

Citation: N. B. Uskova, “The matrix analysis of spectral projections for the perturbed self-adjoint operators”, Sib. Èlektron. Mat. Izv., 16 (2019), 369–405

Citation in format AMSBIB
\Bibitem{Usk19} \by N.~B.~Uskova \paper The matrix analysis of spectral projections for the perturbed self-adjoint operators \jour Sib. \Elektron. Mat. Izv. \yr 2019 \vol 16 \pages 369--405 \mathnet{http://mi.mathnet.ru/semr1064} \crossref{https://doi.org/10.33048/semi.2019.16.022} `