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

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
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\paper Homogeneous Wiener--Hopf Double Integral Equation with Symmetric Kernel in the Conservative Case
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\yr 2019
\vol 106
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\pages 3--12
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\crossref{https://doi.org/10.4213/mzm11911}
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\pages 3--10
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