Geodesic
Homogeneous Wiener--Hopf Double Integral Equation with Symmetric Kernel in the Conservative Case
Matematičeskie zametki, Tome 106 (2019) no. 1, pp. 3-12.

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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. 
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L. G. Arabadzhyan. Homogeneous Wiener--Hopf Double Integral Equation with Symmetric Kernel in the Conservative Case. Matematičeskie zametki, Tome 106 (2019) no. 1, pp. 3-12. http://geodesic.mathdoc.fr/item/MZM_2019_106_1_a0/

[1] L. G. Arabadzhyan, N. B. Engibaryan, “O faktorizatsii kratnykh integralnykh operatorov Vinera–Khopfa”, Dokl. AN SSSR, 291:1 (1986), 11–14 | MR | Zbl

[2] L. G. Arabadzhyan, “O suschestvovanii netrivialnykh reshenii nekotorykh lineinykh i nelineinykh uravnenii tipa svertki”, Ukr. matem. zhurn., 41:12 (1989), 1587–1595 | MR | Zbl

[3] N. B. Engibaryan, A. A. Arutyunyan, “Integralnye uravneniya na polupryamoi s raznostnymi yadrami i nelineinye funktsionalnye uravneniya”, Matem. sb., 97 (139):1 (5) (1975), 35–58 | MR | Zbl

[4] L. G. Arabadzhyan, N. B. Engibaryan, “Uravneniya v svertkakh i nelineinye funktsionalnye uravneniya”, Itogi nauki i tekhn. Ser. Mat. anal., 22, VINITI, M., 1984, 175–244 | MR | Zbl

[5] V. V. Smelov, Lektsii po teorii perenosa neitronov, Atomizdat, M., 1978

[6] Yu. I. Ershov, S. B. Shikhov, Matematicheskie osnovy teorii perenosa, T. 1, Energoatomizdat, M., 1985 | MR

[7] E. Hopf, Mathematical Problems of Radiative Equilibrium, Cambridge Tracts in Math. and Math. Phys., 31, Stechert-Hafner, New York, 1934 | MR

[8] S. Lam, A. Leonard, “Miln's problem for two-dimensional transport in a quarter space”, J. Quant. Spectrosc. Radiat. Transfer., 11:6 (1971), 893–904 | DOI | MR