Geodesic
The inverse and direct problem for equation of the first kind of convolution on the half-line
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1456-1462

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In this paper we study the integral equation first kind of convolution on the semi-infinite interval. The next two tasks are: Task is reconstruction of history. From the integral equation it is required to find two functions $u(t)$ for $t>0$ and $f(t)$ for $0$ for given values of the right side of the equation $f(t)$ for $t>b$ ($u(t)$ — solution of integral equation). The problem of inversion of the integral operator. Uniqueness theorems are proved, necessary and sufficient conditions for solvability are found, explicit formulas for solutions are received. 
@article{SEMR_2017_14_a101,
     author = {A. F. Voronin},
     title = {The inverse and direct problem for equation of the first kind of convolution on the half-line},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1456--1462},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a101/}
}
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A. F. Voronin. The inverse and direct problem for equation of the first kind of convolution on the half-line. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1456-1462. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a101/