We develop a general theory of \( \mathcal{P}\mathcal{T} \)-symmetric operators. Special attention is given to \( \mathcal{P}\mathcal{T} \)-symmetric quasiself-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 the description of nonreal eigenvalues is presented. These abstract results are applied to the Schr¨odinger operator with Coulomb potential on the real axis.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 1, pp. 32–49, January, 2012.
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Kuzhel’, S.O., Patsyuk, O.M. On the theory of \( \mathcal{P}\mathcal{T} \)-symmetric operators. Ukr Math J 64, 35–55 (2012). https://doi.org/10.1007/s11253-012-0628-y
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DOI: https://doi.org/10.1007/s11253-012-0628-y