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

 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
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}