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Ufa Mathematical Journal, 2017, Volume 9, Issue 4, Pages 35–43
DOI: https://doi.org/10.13108/2017-9-4-35
(Mi ufa412)
 

This article is cited in 4 scientific papers (total in 4 papers)

Self-adjoint restrictions of maximal operator on graph

L. K. Zhapsarbayeva, B. E. Kanguzhin, M. N. Konyrkulzhayeva

Al-Farabi Kazakh National University, Al-Farabi av. 71, 050040, Almaty, Kazakhstan
References:
Abstract: In the work we study differential operators on arbitrary geometric graphs without loops. We extend the known results for differential operators on an interval to the differential operators on the graphs. In order to define properly the maximal operator on a given graph, we need to choose a set of boundary vertices. The non-boundary vertices are called interior vertices. We stress that the maximal operator on a graph is determined not only by the given differential expressions on the edges, but also by the Kirchhoff conditions at the interior vertices of the graph. For the introduced maximal operator we prove an analogue of the Lagrange formula. We provide an algorithm for constructing adjoint boundary forms for an arbitrary set of boundary conditions. In the conclusion of the paper, we present a complete description of all self-adjoint restrictions of the maximal operator.
Keywords: Directed graph, Kirchhoff conditions, self-adjoint restriction of an operator, maximal operator.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan 0757/ГФ4
0085/ПЦФ-14
The work is supported by MES of the Republic of Kazakhstan (grant 0757/GF4 and grant 0085/PTsF-14).
Received: 24.07.2017
Bibliographic databases:
Document Type: Article
UDC: 517.927.2
MSC: 34B45, 34L20
Language: English
Original paper language: Russian
Citation: L. K. Zhapsarbayeva, B. E. Kanguzhin, M. N. Konyrkulzhayeva, “Self-adjoint restrictions of maximal operator on graph”, Ufa Math. J., 9:4 (2017), 35–43
Citation in format AMSBIB
\Bibitem{ZhaKanKon17}
\by L.~K.~Zhapsarbayeva, B.~E.~Kanguzhin, M.~N.~Konyrkulzhayeva
\paper Self-adjoint restrictions of maximal operator on graph
\jour Ufa Math. J.
\yr 2017
\vol 9
\issue 4
\pages 35--43
\mathnet{http://mi.mathnet.ru//eng/ufa412}
\crossref{https://doi.org/10.13108/2017-9-4-35}
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\elib{https://elibrary.ru/item.asp?id=30562590}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85038076265}
Linking options:
  • https://www.mathnet.ru/eng/ufa412
  • https://doi.org/10.13108/2017-9-4-35
  • https://www.mathnet.ru/eng/ufa/v9/i4/p36
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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