General information
Latest issue
Impact factor

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Ufimsk. Mat. Zh.:

Personal entry:
Save password
Forgotten password?

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);

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
\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
\jour Ufa Math. J.
\yr 2017
\vol 9
\issue 1
\pages 18--28

Linking options:

    SHARE: FaceBook Twitter Livejournal

    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

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