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