Perturbation of Threshold of the Essential Spectrum of the Schrödinger Operator on the Simplest Graph with a Small Edge
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F19%3A50016364" target="_blank" >RIV/62690094:18470/19:50016364 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/content/pdf/10.1007%2Fs10958-019-04302-0.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007%2Fs10958-019-04302-0.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10958-019-04302-0" target="_blank" >10.1007/s10958-019-04302-0</a>
Alternative languages
Result language
angličtina
Original language name
Perturbation of Threshold of the Essential Spectrum of the Schrödinger Operator on the Simplest Graph with a Small Edge
Original language description
On a star graph consisting of two infinite edges and one small edge, we consider the Schrödinger operators with piecewise-constant potentials on the infinite edges and with a singular potential on the small edge respectively. A δ′-interaction is given at the interior vertex of the graph, and the Dirichlet or Neumann condition is imposed at the boundary vertex of the small edge. We determine the limit boundary conditions, obtain two-term asymptotics for the resolvents in the operator norm and error estimates. The phenomenon of isolated eigenvalues emerging from the threshold of the essential spectrum is discussed. We establish efficient and easily verified sufficient conditions for the existence or absence of such eigenvalues. We establish the holomorphic dependence of the appeared eigenvalues on the edge length and write explicitly the first terms of the Taylor expansions of such eigenvalues.
Czech name
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Czech description
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Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of mathematical sciences
ISSN
1072-3374
e-ISSN
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Volume of the periodical
239
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
248-267
UT code for WoS article
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EID of the result in the Scopus database
2-s2.0-85065441718