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Differential Equations

, Volume 55, Issue 10, pp 1328–1335 | Cite as

Changes in a Finite Part of the Spectrum of the Laplace Operator under Delta-Like Perturbations

  • B. E. KanguzhinEmail author
Partial Differential Equations
  • 6 Downloads

Abstract

We study the spectrum of the Laplace operator in a bounded simply connected domain with the zero Dirichlet condition on the boundary under delta-like perturbations of the operator at an interior point of the domain. We determine the maximal operator for the perturbations and single out a class of invertible restrictions of this operator whose spectra differ from the spectrum of the original operator by a finite (possibly, empty) set. These results can be viewed as transferring some of H. Hochstadt’s results for Sturm-Liouville operators to Laplace operators.

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Notes

Funding

This work was supported in part by the Ministry of Education and Science of the Republic of Kazakhstan, project no. AP05131292.

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Al-Farabi Kazakh National UniversityAlmatyKazakhstan
  2. 2.Institute of Mathematics and Mathematical ModelingAlmatyKazakhstan

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