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, 2012, Volume 203, Issue 6, Pages 893–921
DOI: https://doi.org/10.1070/SM2012v203n06ABEH004247 (Mi sm7872) 		 
Asymptotic estimates for the kernel of the semigroup generated by a perturbation of the biharmonic operator by a potential

S. A. Stepinab

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Institute of Mathematics, University of Bialystok
English version PDF (499 kB)
References:
PDF
HTML
DOI: https://doi.org/10.1070/SM2012v203n06ABEH004247
Abstract: Asymptotic formulae and estimates for the integral kernel of the semigroup generated by a perturbation of the bi-Laplacian by a potential are established by the parametrix method. These formulae are found using an approach which is conceptually close to the probabilistic approach used to calculate the coefficients of a short-time expansion for the heat kernel and based on the representation of this kernel as a Wiener integral. As an application, an asymptotic formula for the regularized trace of the operator semigroup under consideration is found.
Bibliography: 19 titles.
Keywords: operator semigroup, parametrix expansion, Born approximation, regularized trace, short-time asymptotics.
Received: 30.03.2011 and 12.09.2011
Russian version:
Matematicheskii Sbornik, 2012, Volume 203, Number 6, Pages 131–160
DOI: https://doi.org/10.4213/sm7872
Bibliographic databases:
Document Type: Article
UDC: 517.956.8+517.986.7
MSC: Primary 35C20, 35K25; Secondary 35A17, 47F05
Language: English
Original paper language: Russian
Citation: S. A. Stepin, “Asymptotic estimates for the kernel of the semigroup generated by a perturbation of the biharmonic operator by a potential”, Mat. Sb., 203:6 (2012), 131–160; Sb. Math., 203:6 (2012), 893–921
Citation in format AMSBIB
\Bibitem{Ste12}
\by S.~A.~Stepin
\paper Asymptotic estimates for the kernel of the semigroup generated by a~perturbation of the biharmonic operator by a~potential
\jour Mat. Sb.
\yr 2012
\vol 203
\issue 6
\pages 131--160
\mathnet{http://mi.mathnet.ru/sm7872}
\crossref{https://doi.org/10.4213/sm7872}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2984658}
\zmath{https://zbmath.org/?q=an:1251.35014}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2012SbMat.203..893S}
\elib{https://elibrary.ru/item.asp?id=19066516}
\transl
\jour Sb. Math.
\yr 2012
\vol 203
\issue 6
\pages 893--921
\crossref{https://doi.org/10.1070/SM2012v203n06ABEH004247}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000307816000006}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84865028407}
Linking options:
  • https://www.mathnet.ru/eng/sm7872
  • https://doi.org/10.1070/SM2012v203n06ABEH004247
  • https://www.mathnet.ru/eng/sm/v203/i6/p131
    • 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:688
    Russian version PDF:181
    English version PDF:23
    References:72
    First page:27
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024