RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Funktsional. Anal. i Prilozhen.:
Year:
Volume:
Issue:
Page:
Find






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


Funktsional. Anal. i Prilozhen., 2008, Volume 42, Issue 2, Pages 75–78 (Mi faa2904)  

Brief communications

Quasi-Weyl Asymptotics of the Spectrum of the Vector Dirichlet Problem

A. S. Andreev

Popov Higher Naval Academy of Radio Electronics

Abstract: In a space of vector functions, we consider the spectral problem $\mu Au=\mathcal{P}u$, $u=u(x)$, where $A=(A_{jk})$, $j,k=1,…,n$, $A_{jk}=\sum_\alpha a_{\alpha jk}D^{2\alpha}$, $\mathcal{P}=(p_{jk})$, $A\ge c_0>0$, $\mathcal{P}=\mathcal{P}^*$, the $a_{\alpha jk}$ and $p_{jk}$ are constants, $x\in\Omega$, and $\Omega$ is a bounded open set. The boundary conditions correspond to the Dirichlet problem. Let $N_\pm(\mu)$ be the positive and negative spectral counting functions. We establish the asymptotics $N_\pm(\mu)\sim(\operatorname{mes}_m\Omega)\varphi_\pm(\mu)$ as $\mu\to+0$. The functions $\varphi_\pm(\mu)$ are independent of $\Omega$. In the nonelliptic case, these asymptotics are in general different from the classical (Weyl) asymptotics.

Keywords: quasi-Weyl asymptotics, Dirichlet problem, vector Dirichlet problem, nonelliptic differential operator, Weyl formula, Weyl asymptotics

DOI: https://doi.org/10.4213/faa2904

Full text: PDF file (154 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2008, 42:2, 141–143

Bibliographic databases:

UDC: 517.98
Received: 13.06.2006

Citation: A. S. Andreev, “Quasi-Weyl Asymptotics of the Spectrum of the Vector Dirichlet Problem”, Funktsional. Anal. i Prilozhen., 42:2 (2008), 75–78; Funct. Anal. Appl., 42:2 (2008), 141–143

Citation in format AMSBIB
\Bibitem{And08}
\by A.~S.~Andreev
\paper Quasi-Weyl Asymptotics of the Spectrum of the Vector Dirichlet Problem
\jour Funktsional. Anal. i Prilozhen.
\yr 2008
\vol 42
\issue 2
\pages 75--78
\mathnet{http://mi.mathnet.ru/faa2904}
\crossref{https://doi.org/10.4213/faa2904}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2438020}
\zmath{https://zbmath.org/?q=an:1158.35398}
\elib{https://elibrary.ru/item.asp?id=11161693}
\transl
\jour Funct. Anal. Appl.
\yr 2008
\vol 42
\issue 2
\pages 141--143
\crossref{https://doi.org/10.1007/s10688-008-0020-8}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000257324700008}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-46249114088}


Linking options:
  • http://mi.mathnet.ru/eng/faa2904
  • https://doi.org/10.4213/faa2904
  • http://mi.mathnet.ru/eng/faa/v42/i2/p75

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
    Number of views:
    This page:259
    Full text:105
    References:35
    First page:8

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020