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

  • S. A. Kuzhel'
  • O. M. Patsyuk Iн-т математики НАН України, Київ


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.
How to Cite
Kuzhel’, S. A., and O. M. Patsyuk. “On the Theory of $\mathcal{PT}$-Symmetric Operatorss”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 1, Jan. 2012, pp. 32-49, https://umj.imath.kiev.ua/index.php/umj/article/view/2554.
Research articles