Geodesic
Homogeneous conservative Wiener--Hopf equation
Sbornik. Mathematics, Tome 198 (2007) no. 9, pp. 1341-1350

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The existence of a $P^*$-solution of the homogeneous generalized Wiener–Hopf equation $$ S(x)=\int_{-\infty}^xS(x-y)\,F(dy),\qquad x\geqslant0, $$ is proved, where $F$ is a probability distribution of recurrent type in $\mathbb R$. Asymptotic properties of this solution are established. Bibliography: 10 titles. 
@article{SM_2007_198_9_a6,
     author = {M. S. Sgibnev},
     title = {Homogeneous conservative {Wiener--Hopf} equation},
     journal = {Sbornik. Mathematics},
     pages = {1341--1350},
     publisher = {mathdoc},
     volume = {198},
     number = {9},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2007_198_9_a6/}
}
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M. S. Sgibnev. Homogeneous conservative Wiener--Hopf equation. Sbornik. Mathematics, Tome 198 (2007) no. 9, pp. 1341-1350. http://geodesic.mathdoc.fr/item/SM_2007_198_9_a6/