Spectral enclosures for non-self-adjoint extensions of symmetric operators

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F18%3A00492485" target="_blank" >RIV/61389005:_____/18:00492485 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jfa.2018.04.005" target="_blank" >http://dx.doi.org/10.1016/j.jfa.2018.04.005</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2018.04.005" target="_blank" >10.1016/j.jfa.2018.04.005</a>

Result language
angličtina
Original language name
Spectral enclosures for non-self-adjoint extensions of symmetric operators
Original language description
The spectral properties of non-self-adjoint extensions A([B] )of a symmetric operator in a Hilbert space are studied with the help of ordinary and quasi boundary triples and the corresponding Weyl functions. These extensions are given in terms of abstract boundary conditions involving an (in general non-symmetric) boundary operator B. In the abstract part of this paper, sufficient conditions for sectoriality and m-sectoriality as well as sufficient conditions for A( [B] )to have a non-empty resolvent set are provided in terms of the parameter B and the Weyl function. Special attention is paid to Weyl functions that decay along the negative real line or inside some sector in the complex plane, and spectral enclosures for A([B]) are proved in this situation. The abstract results are applied to elliptic differential operators with local and non-local Robin boundary conditions on unbounded domains, to Schrodinger operators with delta-potentials of complex strengths supported on unbounded hypersurfaces or infinitely many points on the real line, and to quantum graphs with non-self-adjoint vertex couplings.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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