RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Ufimsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






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


Ufimsk. Mat. Zh., 2017, Volume 9, Issue 1, Pages 18–28 (Mi ufa362)  

This article is cited in 3 scientific papers (total in 3 papers)

On deficiency index for some second order vector differential operators

I. N. Braeutigama, K. A. Mirzoevb, T. A. Safonovaa

a Northern (Arctic) Federal University named after M. V. Lomonosov, Severnaya Dvina Emb. 17, 163002, Arkhangelsk, Russia
b Lomonosov Moscow State University, Leninskie Gory, 1, 119991, Moscow, Russia

Abstract: In this paper we consider the operators generated by the second order matrix linear symmetric quasi-differential expression
$$ l[y]=-(P(y'-Ry))'-R^*P(y'-Ry)+Qy $$
on the set $[1,+\infty)$, where $P^{-1}(x)$, $Q(x)$ are Hermitian matrix functions and $R(x)$ is a complex matrix function of order $n$ with entries $p_{ij}(x),q_{ij}(x),r_{ij}(x)\in L^1_{loc}[1,+\infty)$ ($i,j=1,2,…,n$). We describe the minimal closed symmetric operator $L_0$ generated by this expression in the Hilbert space $L^2_n[1,+\infty)$. For this operator we prove an analogue of the Orlov's theorem on the deficiency index of linear scalar differential operators.

Keywords: quasi-derivative, quasi-differential expression, minimal closed symmetric differential operator, deficiency numbers, asymptotic of the fundamental system of solutions.

Funding Agency Grant Number
German Academic Exchange Service (DAAD) 1.728.2016/DAAD
Russian Science Foundation 14-11-00754
Ministry of Education and Science of the Russian Federation МК-3941.2015.1
The first author is supported by the grant of the Ministery of Educations and Science of Russia and German Academic Exchange Service (DAAD) under the program “Mikhail Lomonosov” (no. 1.728.2016/DAAD). The second author is supported by the grant of RSF (no. 14-11-00754). The third author is supported by Ministery of Educations and Science of Russia (the grant of the President of Russia no. MK-3941.2015.1).


Full text: PDF file (554 kB)
References: PDF file   HTML file

English version:
Ufa Mathematical Journal, 2017, 9:1, 18–28 (PDF, 359 kB); https://doi.org/10.13108/2017-9-1-18

Bibliographic databases:

Document Type: Article
UDC: 517.984
MSC: 34A30, 34L05, 47E05
Received: 24.05.2016

Citation: I. N. Braeutigam, K. A. Mirzoev, T. A. Safonova, “On deficiency index for some second order vector differential operators”, Ufimsk. Mat. Zh., 9:1 (2017), 18–28; Ufa Math. J., 9:1 (2017), 18–28

Citation in format AMSBIB
\Bibitem{BraMirSaf17}
\by I.~N.~Braeutigam, K.~A.~Mirzoev, T.~A.~Safonova
\paper On deficiency index for some second order vector differential operators
\jour Ufimsk. Mat. Zh.
\yr 2017
\vol 9
\issue 1
\pages 18--28
\mathnet{http://mi.mathnet.ru/ufa362}
\elib{http://elibrary.ru/item.asp?id=29009892}
\transl
\jour Ufa Math. J.
\yr 2017
\vol 9
\issue 1
\pages 18--28
\crossref{https://doi.org/10.13108/2017-9-1-18}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000411736500002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85018786120}


Linking options:
  • http://mi.mathnet.ru/eng/ufa362
  • http://mi.mathnet.ru/eng/ufa/v9/i1/p18

    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

    This publication is cited in the following articles:
    1. Budyika V., Malamud M., Posilicano A., “Nonrelativistic Limit For 2P X 2P-Dirac Operators With Point Interactions on a Discrete Set”, Russ. J. Math. Phys., 24:4 (2017), 426–435  crossref  mathscinet  zmath  isi  scopus
    2. I. N. Braeutigam, K. A. Mirzoev, “Asymptotics of Solutions of Matrix Differential Equations with Nonsmooth Coefficients”, Math. Notes, 104:1 (2018), 150–155  mathnet  crossref  crossref  isi  elib
    3. N. N. Konechnaja, K. A. Mirzoev, A. A. Shkalikov, “On the Asymptotic Behavior of Solutions to Two-Term Differential Equations with Singular Coefficients”, Math. Notes, 104:2 (2018), 244–252  mathnet  crossref  crossref  isi  elib
  • Уфимский математический журнал
    Number of views:
    This page:2338
    Full text:37
    References:12

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