RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






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


Mat. Zametki, 2017, Volume 102, Issue 6, Pages 931–937 (Mi mz11470)  

Basis Property of Eigen- and Associated Functions of an Operator with Nondense Domain of Definition in the Example of the Orr–Sommerfeld problem

E. A. Shiryaev

Polytechnical museum, Moscow

Abstract: In the paper, we propose a method for proving the unconditional basis property of eigen- and associated functions of an integro-differential operator defined on a nondense domain of definition. In particular, we obtain a new simpler proof of the unconditional basis property of eigen- and associated functions of the spectral Orr–Sommerfeld problem, well-known in hydromechanics, which reduces to the eigenvalue problem for the operator under study.

Keywords: Orr–Sommerfeld problem, pencils of differential operators, Riesz basis, unconditional basis, Sobolev spaces.

Funding Agency Grant Number
Russian Science Foundation 14-11-00754
This work was supported by the Russian Science Foundation under grant 14-11-00754.


DOI: https://doi.org/10.4213/mzm11470

Full text: PDF file (443 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Mathematical Notes, 2017, 102:6, 867–872

Bibliographic databases:

Document Type: Article
UDC: 517.984
Received: 30.10.2016
Revised: 24.09.2017

Citation: E. A. Shiryaev, “Basis Property of Eigen- and Associated Functions of an Operator with Nondense Domain of Definition in the Example of the Orr–Sommerfeld problem”, Mat. Zametki, 102:6 (2017), 931–937; Math. Notes, 102:6 (2017), 867–872

Citation in format AMSBIB
\Bibitem{Shi17}
\by E.~A.~Shiryaev
\paper Basis Property of Eigen- and Associated Functions of an Operator with Nondense Domain of Definition in the Example of the Orr--Sommerfeld problem
\jour Mat. Zametki
\yr 2017
\vol 102
\issue 6
\pages 931--937
\mathnet{http://mi.mathnet.ru/mz11470}
\crossref{https://doi.org/10.4213/mzm11470}
\elib{http://elibrary.ru/item.asp?id=30737898}
\transl
\jour Math. Notes
\yr 2017
\vol 102
\issue 6
\pages 867--872
\crossref{https://doi.org/10.1134/S0001434617110268}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000418838500026}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85039459871}


Linking options:
  • http://mi.mathnet.ru/eng/mz11470
  • https://doi.org/10.4213/mzm11470
  • http://mi.mathnet.ru/eng/mz/v102/i6/p931

    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
  • Математические заметки Mathematical Notes
    Number of views:
    This page:103
    References:15
    First page:17

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019