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On stable $\mathcal{C}$-symmetries for a class of $\mathcal{PT}$-symmetric operators


Recently, much attention is paid to the consideration of physical models described by $\mathcal{PT}$-symmetric Hamiltonians. In this paper, we establish a necessary and sufficient condition for existence of a stable $\mathcal{C}$-symmetry for a class of $\mathcal{PT}$-symmetric extensions of a symmetric operator $S$ with deficiency indices $(2,2)$.

Key words: PT -symmetric Hamiltonians, exact PT -symmetry, real spectrum, stable C-symmetry, extension theory of symmetric operators, boundary triplets, Krein spaces, Clifford algebra.

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TitleOn stable $\mathcal{C}$-symmetries for a class of $\mathcal{PT}$-symmetric operators
SourceMethods Funct. Anal. Topology, Vol. 19 (2013), no. 1, 73-79
MathSciNet   MR3088320
zbMATH 1289.47047
Milestones  Received 21/11/2012; Revised 01/12/2012
CopyrightThe Author(s) 2013 (CC BY-SA)

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O. M. Patsyuck
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine 

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O. M. Patsyuck, On stable $\mathcal{C}$-symmetries for a class of $\mathcal{PT}$-symmetric operators, Methods Funct. Anal. Topology 19 (2013), no. 1, 73-79.


@article {MFAT671,
    AUTHOR = {Patsyuck, O. M.},
     TITLE = {On stable $\mathcal{C}$-symmetries for a class of $\mathcal{PT}$-symmetric operators},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {19},
      YEAR = {2013},
    NUMBER = {1},
     PAGES = {73-79},
      ISSN = {1029-3531},
  MRNUMBER = {MR3088320},
 ZBLNUMBER = {1289.47047},
       URL = {},

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