Non self-adjoint correct restrictions and extensions with real spectrum

B. N. Biyarov; Z. A. Zakarieva; G. K. Abdrasheva

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arXiv · 2101.09959

Non self-adjoint correct restrictions and extensions with real spectrum

B. N. Biyarov·Z. A. Zakarieva·G. K. Abdrasheva

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Abstract

The work is devoted to the study of the similarity of a correct restriction to some self-adjoint operator in the case when the minimal operator is symmetric. The resulting theorem was applied to the Sturm-Liouville operator and the Laplace operator. It is shown that the spectrum of a non self-adjoint singularly perturbed operator is real and the corresponding system of eigenvectors forms a Riesz basis.

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BibTeX RIS

B. N. Biyarov, Z. A. Zakarieva, G. K. Abdrasheva. 2021-01-25. Non self-adjoint correct restrictions and extensions with real spectrum. https://arxiv.org/abs/2101.09959

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