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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Functional Analysis

ISSN

0022-1236

e-ISSN

—

Svazek periodika

275

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

81

Strana od-do

1808-1888

Kód UT WoS článku

000441371200006

EID výsledku v databázi Scopus

2-s2.0-85046679721