RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
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. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb., 1998, Volume 189, Number 12, Pages 59–72 (Mi msb360)  

This article is cited in 9 scientific papers (total in 9 papers)

Renewal theorems for a system of integral equations

N. B. Engibaryan

Byurakan Astrophysical Observatory, National Academy of Sciences of Armenia

Abstract: The system of renewal integral equations
$$ \varphi _i(x)=g_i(x)+\sum _{j=1}^m\int _0^xu_{ij}(x-t)\varphi _j(t) dt, \qquad i=1,…,m, $$
is considered, where the matrix-valued function $u=(u_{ij})$ satisfies the condition of conservativeness $0\leqslant u_{ij}\in L_1^+\equiv L_1(0;\infty)$, and the matrix $A=\int _0^\infty u(x) dx$ is irreducible and of spectral radius.
The existence of a limit at $+\infty$ of the solution $\varphi =(\varphi _1,…,\varphi _m)^T$ is established in the case when the vector-valued function $g=(g_1,…,g_m)^T\in L_1^m$ is bounded and $g(+\infty )=0$. This limit is evaluated. The structure of $\phi$ for $g\in L_1^m$ is determined; namely, $\varphi (x)=\mu +\rho _0(x)+\psi(x)$, where $\rho _0\in C_0^m$ and $\psi \in L_1^m$. A similar formula for the resolvent matrix-valued function is obtained.

DOI: https://doi.org/10.4213/sm360

Full text: PDF file (249 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 1998, 189:12, 1795–1808

Bibliographic databases:

UDC: 517.9+519.24
MSC: 45E10, 45F15
Received: 02.04.1997 and 23.10.1997

Citation: N. B. Engibaryan, “Renewal theorems for a system of integral equations”, Mat. Sb., 189:12 (1998), 59–72; Sb. Math., 189:12 (1998), 1795–1808

Citation in format AMSBIB
\Bibitem{Eng98}
\by N.~B.~Engibaryan
\paper Renewal theorems for a~system of integral equations
\jour Mat. Sb.
\yr 1998
\vol 189
\issue 12
\pages 59--72
\mathnet{http://mi.mathnet.ru/msb360}
\crossref{https://doi.org/10.4213/sm360}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1686012}
\zmath{https://zbmath.org/?q=an:0932.45005}
\transl
\jour Sb. Math.
\yr 1998
\vol 189
\issue 12
\pages 1795--1808
\crossref{https://doi.org/10.1070/sm1998v189n12ABEH000360}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000080632300011}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0032235911}


Linking options:
  • http://mi.mathnet.ru/eng/msb360
  • https://doi.org/10.4213/sm360
  • http://mi.mathnet.ru/eng/msb/v189/i12/p59

    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. M. S. Sgibnev, “Stone decomposition for a matrix renewal measure on a half-line”, Sb. Math., 192:7 (2001), 1025–1033  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. N. B. Engibaryan, “Conservative systems of integral convolution equations on the half-line and the entire line”, Sb. Math., 193:6 (2002), 847–867  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. N. B. Engibaryan, “Asymptotic and structural theorems for the Markov renewal equation”, Theory Probab. Appl., 48:1 (2004), 80–92  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. De Saporta B., “Renewal theorem for a system of renewal equations”, Ann. Inst. H. Poincaré Probab. Statist., 39:5 (2003), 823–838  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. Sgibnev, MS, “Systems of renewal-type integral equations on the line”, Differential Equations, 40:1 (2004), 137  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    6. Yengibarian, NB, “Factorization of Markov chains”, Journal of Theoretical Probability, 17:2 (2004), 459  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    7. M.S. Sgibnev, Publ. Inst. Math. (Belgr.), 76:90 (2004), 149  crossref  mathscinet  zmath
    8. M. S. Sgibnev, “The matrix analogue of the Blackwell renewal theorem on the real line”, Sb. Math., 197:3 (2006), 369–386  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. Kh. A. Khachatryan, “Solvability of vector integro-differential equations of convolution type on the semiaxis”, J Contemp Mathemat Anal, 43:5 (2008), 305  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:389
    Full text:138
    References:67
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021