Abstract
We consider a self-adjoint differential operator in Hilbert space. Then the domain of the operator is changed by the perturbation of the boundary conditions so that a given neighborhood “is cleared” from the points of the spectrum of the perturbed operator. For the Sturm–Liouville operator on the segment and the Laplace operator on the square such a possibility is attained via integral perturbations of boundary conditions.
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Original Russian Text ©B.E. Kanguzhin, D. Dauitbek, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 2, pp. 14–21.
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Kanguzhin, B.E., Dauitbek, D. A maximum of the first eigenvalue of semibounded differential operator with a parameter. Russ Math. 61, 10–16 (2017). https://doi.org/10.3103/S1066369X17020025
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DOI: https://doi.org/10.3103/S1066369X17020025