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Mat. Zametki, 1997, Volume 62, Issue 3, Pages 323–331 (Mi mz1614)  

This article is cited in 5 scientific papers (total in 5 papers)

On a conservative integral equation with two kernels

L. G. Arabadzhyan

Byurakan Astrophysical Observatory, National Academy of Sciences of Armenia

Abstract: We study the solvability of the integral equation
$$ f(x)=g(x)+\int_0^\infty T_1(x-t)f(t) dt+\int_{-\infty}^0T_2(x-t)f(t) dt,\qquad x\in\mathbb R, $$
where $f\in L_1^{\operatorname{loc}}(\mathbb R)$ is the unknown function and $g$, $T_1$ and $T_2$ are given functions satisfying the conditions
$$ g\in L_1(\mathbb R),\quad 0\le T_j\in L_1(\mathbb R),\quad \int_{-\infty}^\infty T_j(t) dt=1,\qquad j=1,2. $$
Most attention is paid to the nontrivial solvability of the homogeneous equation
$$ s(x)=\int_0^\infty T_1(x-t)s(t) dt+\int_{-\infty}^0T_2(x-t)s(t) dt,\qquad x\in\mathbb R. $$


DOI: https://doi.org/10.4213/mzm1614

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English version:
Mathematical Notes, 1997, 62:3, 271–277

Bibliographic databases:

UDC: 517
Received: 14.12.1995

Citation: L. G. Arabadzhyan, “On a conservative integral equation with two kernels”, Mat. Zametki, 62:3 (1997), 323–331; Math. Notes, 62:3 (1997), 271–277

Citation in format AMSBIB
\Bibitem{Ara97}
\by L.~G.~Arabadzhyan
\paper On a conservative integral equation with two kernels
\jour Mat. Zametki
\yr 1997
\vol 62
\issue 3
\pages 323--331
\mathnet{http://mi.mathnet.ru/mz1614}
\crossref{https://doi.org/10.4213/mzm1614}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1620042}
\zmath{https://zbmath.org/?q=an:0914.45003}
\transl
\jour Math. Notes
\yr 1997
\vol 62
\issue 3
\pages 271--277
\crossref{https://doi.org/10.1007/BF02360867}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000072500900001}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. von Wolfersdorf, L, “A class of linear integral equations and systems with sum and difference kernel”, Zeitschrift fur Analysis und Ihre Anwendungen, 22:3 (2003), 647  mathscinet  zmath  isi
    2. Wolfersdorf, LV, “On a class of nonlinear cross-correlation equations”, Mathematische Nachrichten, 269-70 (2004), 231  crossref  mathscinet  zmath  isi  scopus
    3. A. G. Barsegyan, “O reshenii uravneniya s dvumya yadrami, predstavlennymi cherez eksponenty”, Ufimsk. matem. zhurn., 3:4 (2011), 28–38  mathnet  zmath
    4. Ter-Avetisyan V.V., “On Dual Integral Equations in the Semiconservative Case”, J. Contemp. Math. Anal.-Armen. Aca., 47:2 (2012), 62–69  crossref  mathscinet  zmath  isi  scopus
    5. Barsegyan A.G., “On the Solution of the Convolution Equation with Two Kernels”, Differ. Equ., 48:5 (2012), 756–759  crossref  mathscinet  zmath  isi  elib  scopus
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