Non self-adjoint correct restrictions and extensions with real spectrum

2021/01/25 by B. N. Biyarov, Biyarov, B. N., Zakarieva, Z. A. +1
Mathematics · #35B25 #47A55 #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2101.09959

openalex publication_date 2021/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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