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

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About: On the Similarity of Sturm-Liouville Operators with Non-Hermitian Boundary Conditions to Self-Adjoint and Normal Operators Goto Sponge NotDistinct Permalink

An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://link.springer.com/article/10.1007%2Fs11785-013-0301-y
Description	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 %22charge conjugation%22 operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem. 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 %22charge conjugation%22 operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem. (en)
Title	On the Similarity of Sturm-Liouville Operators with Non-Hermitian Boundary Conditions to Self-Adjoint and Normal Operators On the Similarity of Sturm-Liouville Operators with Non-Hermitian Boundary Conditions to Self-Adjoint and Normal Operators (en)
skos:prefLabel	On the Similarity of Sturm-Liouville Operators with Non-Hermitian Boundary Conditions to Self-Adjoint and Normal Operators On the Similarity of Sturm-Liouville Operators with Non-Hermitian Boundary Conditions to Self-Adjoint and Normal Operators (en)
skos:notation	RIV/68407700:21340/14:00229041!RIV15-MSM-21340___
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GAP203/11/0701), P(LC06002), P(LC527)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Siegl, Petr Železný, Jakub
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta jaderná a fyzikálně inženýrská
http://linked.open...dnocenehoVysledku	34515
http://linked.open...ai/riv/idVysledku	RIV/68407700:21340/14:00229041
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	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 (en)
http://linked.open.../riv/klicoveSlovo	C operator Complex symmetric operator Discrete spectral operator Hilbert-Schmidt operators Metric operator Non-symmetric Robin boundary conditions Similarity to normal or self-adjoint operators Sturm-Liouville operators PT-symmetry
http://linked.open...odStatuVydavatele	CH - Švýcarská konfederace
http://linked.open...ontrolniKodProRIV	[D8EBB37259FE]
http://linked.open...i/riv/nazevZdroje	COMPLEX ANALYSIS AND OPERATOR THEORY
http://linked.open...in/vavai/riv/obor	BE
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Guided Quantum Dynamics Doppler Institute for Mathematical Physics and Applied Mathematics Center for Particle Physics
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	8
http://linked.open...iv/tvurceVysledku	Siegl, Petr Železný, Jakub Krejčiřík, D.
http://linked.open...ain/vavai/riv/wos	000329229000014
issn	1661-8254
number of pages	27 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/s11785-013-0301-y
http://localhost/t...ganizacniJednotka	21340

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