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Mat. Zametki, 2019, Volume 106, Issue 1, Pages 3–12 (Mi mz11911)  

This article is cited in 1 scientific paper (total in 1 paper)

Homogeneous Wiener–Hopf Double Integral Equation with Symmetric Kernel in the Conservative Case

L. G. Arabadzhyanab

a Institute of Mathematics, National Academy of Sciences of Armenia
b Armenian State Teachers' Training University named after Khachatur Abovian

Abstract: We establish nontrivial solvability conditions for the homogeneous double integral equation
$$ S(x,y)=\int^\infty_0 \int^\infty_0 K(x-x',y-y')S(x',y') dx' dy',\qquad (x,y)\in\mathbb R_+\times \mathbb R_+, $$
where $\mathbb R_+\equiv[0,+\infty)$, under the assumption that the given function $K$ satisfies the conservativity conditions
$$ 0\le K\in L_1,\qquad \iint_{\mathbb R^2}K(x,y) dx dy=1 $$
and some additional conditions on its first and second moments.

Keywords: Wiener–Hopf double integral equation, conservativity conditions, factorization of the integral operator.

DOI: https://doi.org/10.4213/mzm11911

Full text: PDF file (470 kB)
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English version:
Mathematical Notes, 2019, 106:1, 3–10

Bibliographic databases:

UDC: 517.9
Received: 29.12.2017
Revised: 08.07.2018

Citation: L. G. Arabadzhyan, “Homogeneous Wiener–Hopf Double Integral Equation with Symmetric Kernel in the Conservative Case”, Mat. Zametki, 106:1 (2019), 3–12; Math. Notes, 106:1 (2019), 3–10

Citation in format AMSBIB
\Bibitem{Ara19}
\by L.~G.~Arabadzhyan
\paper Homogeneous Wiener--Hopf Double Integral Equation with Symmetric Kernel in the Conservative Case
\jour Mat. Zametki
\yr 2019
\vol 106
\issue 1
\pages 3--12
\mathnet{http://mi.mathnet.ru/mz11911}
\crossref{https://doi.org/10.4213/mzm11911}
\elib{https://elibrary.ru/item.asp?id=38487775}
\transl
\jour Math. Notes
\yr 2019
\vol 106
\issue 1
\pages 3--10
\crossref{https://doi.org/10.1134/S0001434619070010}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000483778800001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85071453399}


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  • http://mi.mathnet.ru/eng/mz11911
  • https://doi.org/10.4213/mzm11911
  • http://mi.mathnet.ru/eng/mz/v106/i1/p3

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    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. L. G. Arabadzhyan, G. L. Arabajyan, “Nontrivial solvability of the homogeneous Wiener–Hopf multiple integral equation in the conservative case and the Peierls equation”, Theoret. and Math. Phys., 204:1 (2020), 957–965  mathnet  crossref  crossref  isi
  • Математические заметки Mathematical Notes
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