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On the Similarity of Sturm-Liouville Operators with Non-Hermitian Boundary Conditions to Self-Adjoint and Normal Operators
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SYSNO ASEP 0425780 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On the Similarity of Sturm-Liouville Operators with Non-Hermitian Boundary Conditions to Self-Adjoint and Normal Operators Author(s) Krejčiřík, David (UJF-V) RID
Siegl, Petr (UJF-V) RID
Železný, Jakub (UJF-V)Number of authors 3 Source Title Complex Analysis and Operator Theory - ISSN 1661-8254
Roč. 8, č. 1 (2014), s. 255-281Number of pages 27 s. Publication form Print - P Language eng - English Country CH - Switzerland Keywords 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 Subject RIV BE - Theoretical Physics R&D Projects LC06002 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) LC527 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) GAP203/11/0701 GA ČR - Czech Science Foundation (CSF) Institutional support UJF-V - RVO:61389005 UT WOS 000329229000014 DOI 10.1007/s11785-013-0301-y Annotation 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. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2015
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