Počet záznamů: 1  

On the Similarity of Sturm-Liouville Operators with Non-Hermitian Boundary Conditions to Self-Adjoint and Normal Operators

  1. 1. 0425780 - UJF-V 2015 RIV CH eng J - Článek v odborném periodiku
    Krejčiřík, David - Siegl, Petr - Železný, Jakub
    On the Similarity of Sturm-Liouville Operators with Non-Hermitian Boundary Conditions to Self-Adjoint and Normal Operators.
    Complex Analysis and Operator Theory. Roč. 8, č. 1 (2014), s. 255-281. ISSN 1661-8254
    Grant CEP: GA MŠk LC06002; GA MŠk LC527; GA ČR GAP203/11/0701
    Grant ostatní:GA ČR(CZ) GD202/08/H072
    Institucionální podpora: RVO:61389005
    Klíčová slova: Sturm-Liouville operators * non-symmetric Robin boundary conditions * similarity to normal or self-adjoint operators * discrete spectral operator * complex symmetric operator * PT-symmetry * metric operator * C operator * Hilbert-Schmidt operators
    Kód oboru RIV: BE - Teoretická fyzika
    Impakt faktor: 0.545, rok: 2014

    We consider one-dimensional Schrodinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrodinger operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.
    Trvalý link: http://hdl.handle.net/11104/0231575