Exotic eigenvalues and analytic resolvent for a graph with a shrinking edge

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F23%3A50021224" target="_blank" >RIV/62690094:18470/23:50021224 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s13324-023-00853-3" target="_blank" >https://link.springer.com/article/10.1007/s13324-023-00853-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13324-023-00853-3" target="_blank" >10.1007/s13324-023-00853-3</a>

Result language
angličtina
Original language name
Exotic eigenvalues and analytic resolvent for a graph with a shrinking edge
Original language description
We consider a metric graph consisting of two edges, one of which has length ε which we send to zero. On this graph we study the resolvent and spectrum of the Laplacian subject to a general vertex condition at the connecting vertex. Despite the singular nature of the perturbation (by a short edge), we find that the resolvent depends analytically on the parameter ε . In contrast, the negative eigenvalues escape to minus infinity at rates that could be fractional, namely, ε , ε- 2 / 3 or ε- 1 . These rates take place when the corresponding eigenfunction localizes, respectively, only on the long edge, on both edges, or only on the short edge. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
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
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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