Sbornik: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sbornik: Mathematics, 2008, Volume 199, Issue 7, Pages 1071–1087
DOI: https://doi.org/10.1070/SM2008v199n07ABEH003954
(Mi sm3892)
 

This article is cited in 6 scientific papers (total in 6 papers)

The kernel of Laplace-Beltrami operators with zero-radius potential or on decorated graphs

A. A. Tolchennikov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
Abstract: An isomorphism is described for the kernel of the Laplace operator $\Delta^{\!\Lambda}$ (determined by a Lagrangian plane $\Lambda\subset\mathbb C^k\oplus\mathbb C^k$) with potential $\sum_{j=1}^kc_j\delta_{q_j}(x)$ on a manifold. The isomorphism is given by $\Gamma\colon\ker\Delta^{\!\Lambda}\to\Lambda\cap\nobreak L$, where $L$ is an (explicitly calculated) Lagrangian plane. A similar isomorphism also holds for the Laplace operator on a decorated graph. The inequality $1\le\dim\ker\Delta^{\!\Lambda_0}\le n-v+2$ is established for the Laplace operator $\Delta^{\!\Lambda_0}$ on a decorated graph (obtained by decorating a connected finite graph with $n$ edges and $v$ vertices) with ‘continuity’ conditions. It is also shown that the quantity $n-v+1-\dim\ker\Delta^{\!\Lambda_0}$ does not decrease when new edges or manifolds are added.
Bibliography: 12 titles.
Received: 31.05.2007 and 01.04.2008
Russian version:
Matematicheskii Sbornik, 2008, Volume 199, Number 7, Pages 123–138
DOI: https://doi.org/10.4213/sm3892
Bibliographic databases:
UDC: 517.984.68+515.168.5+517.956.227
MSC: 47B25, 58J05
Language: English
Original paper language: Russian
Citation: A. A. Tolchennikov, “The kernel of Laplace-Beltrami operators with zero-radius potential or on decorated graphs”, Mat. Sb., 199:7 (2008), 123–138; Sb. Math., 199:7 (2008), 1071–1087
Citation in format AMSBIB
\Bibitem{Tol08}
\by A.~A.~Tolchennikov
\paper The kernel of Laplace-Beltrami operators
with zero-radius potential or on decorated graphs
\jour Mat. Sb.
\yr 2008
\vol 199
\issue 7
\pages 123--138
\mathnet{http://mi.mathnet.ru/sm3892}
\crossref{https://doi.org/10.4213/sm3892}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2488226}
\elib{https://elibrary.ru/item.asp?id=20425544}
\transl
\jour Sb. Math.
\yr 2008
\vol 199
\issue 7
\pages 1071--1087
\crossref{https://doi.org/10.1070/SM2008v199n07ABEH003954}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000260697900007}
\elib{https://elibrary.ru/item.asp?id=14481556}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-57049136675}
Linking options:
  • https://www.mathnet.ru/eng/sm3892
  • https://doi.org/10.1070/SM2008v199n07ABEH003954
  • https://www.mathnet.ru/eng/sm/v199/i7/p123
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:634
    Russian version PDF:398
    English version PDF:13
    References:70
    First page:14
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024