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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 498, Pages 21–26
DOI: https://doi.org/10.31857/S268695432103005X
(Mi danma171)
 

This article is cited in 3 scientific papers (total in 3 papers)

MATHEMATICS

Quantum graphs with small edges: holomorphy of resolvents

D. I. Borisovabc

a Institute of Mathematics, Ufa Federal Research Center, Russian Academy of Sciences, Ufa, Russia
b Bashkir State Pedagogical University, Ufa, Russia
c University of Hradec Králové, Czech Republic
Full-text PDF (242 kB) Citations (3)
References:
Abstract: We consider a general scalar self-adjoint elliptic second order operator with general boundary conditions on an arbitrary metric graph containing a subgraph with edges of lengths proportional to a small parameter. We show that the resolvent of such operator is holomorphic in the small parameter and provide its representations by Taylor series. The coefficients of the series are found rather explicitly.
Keywords: graph, small edge, resolvent, holomorphy in a small parameter.
Funding agency Grant number
Russian Science Foundation 20-11-19995
This work was supported by the Russian Science Foundation, project no. 20-11-19995.
Presented: I. A. Taimanov
Received: 30.03.2021
Revised: 30.03.2021
Accepted: 05.04.2021
English version:
Doklady Mathematics, 2021, Volume 103, Issue 3, Pages 113–117
DOI: https://doi.org/10.1134/S1064562421030054
Bibliographic databases:
Document Type: Article
UDC: 517.984.5
Language: Russian
Citation: D. I. Borisov, “Quantum graphs with small edges: holomorphy of resolvents”, Dokl. RAN. Math. Inf. Proc. Upr., 498 (2021), 21–26; Dokl. Math., 103:3 (2021), 113–117
Citation in format AMSBIB
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\by D.~I.~Borisov
\paper Quantum graphs with small edges: holomorphy of resolvents
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2021
\vol 498
\pages 21--26
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\transl
\jour Dokl. Math.
\yr 2021
\vol 103
\issue 3
\pages 113--117
\crossref{https://doi.org/10.1134/S1064562421030054}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85112370475}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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