2019
Том 71
№ 7

# On the theory of $\mathcal{PT}$-symmetric operatorss

Abstract

This article develops a general theory of $\mathcal{PT}$-symmetric operators. Special attention is given to $\mathcal{PT}$-symmetric quasi-self-adjoint extensions of symmetric operator with deficiency indices 〈 2, 2 〉. For these extensions, the possibility of their interpretation as self-adjoint operators in Krein spaces is investigated, and a description of nonreal eigenvalues is given. These abstract results are applied to the Schrodinger operator with Coulomb potential on the real axis.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 1, pp 35-55.

Citation Example: Kuzhel' S. A., Patsyuk O. M. On the theory of $\mathcal{PT}$-symmetric operatorss // Ukr. Mat. Zh. - 2012. - 64, № 1. - pp. 32-49.

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