Spectra of Elliptic Operators on Quantum Graphs with Small Edges
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F21%3A50018608" target="_blank" >RIV/62690094:18470/21:50018608 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2227-7390/9/16/1874" target="_blank" >https://www.mdpi.com/2227-7390/9/16/1874</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/math9161874" target="_blank" >10.3390/math9161874</a>
Alternative languages
Result language
angličtina
Original language name
Spectra of Elliptic Operators on Quantum Graphs with Small Edges
Original language description
We consider a general second order self-adjoint elliptic operator on an arbitrary metric graph, to which a small graph is glued. This small graph is obtained via rescaling a given fixed graph gamma by a small positive parameter epsilon. The coefficients in the differential expression are varying, and they, as well as the matrices in the boundary conditions, can also depend on epsilon and we assume that this dependence is analytic. We introduce a special operator on a certain extension of the graph gamma and assume that this operator has no embedded eigenvalues at the threshold of its essential spectrum. It is known that under such assumption the perturbed operator converges to a certain limiting operator. Our main results establish the convergence of the spectrum of the perturbed operator to that of the limiting operator. The convergence of the spectral projectors is proved as well. We show that the eigenvalues of the perturbed operator converging to limiting discrete eigenvalues are analytic in epsilon and the same is true for the associated perturbed eigenfunctions. We provide an effective recurrent algorithm for determining all coefficients in the Taylor series for the perturbed eigenvalues and eigenfunctions.
Czech name
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Czech description
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Classification
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
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
MATHEMATICS
ISSN
2227-7390
e-ISSN
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Volume of the periodical
9
Issue of the periodical within the volume
16
Country of publishing house
CH - SWITZERLAND
Number of pages
24
Pages from-to
"Article Number: 1874"
UT code for WoS article
000689404600001
EID of the result in the Scopus database
2-s2.0-85112396760