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. 
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/
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[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