Geodesic
Recovery solutions of the Volterra equation of the first kind of convolution on the half with incomplete data
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 464-471.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we study the integral equation Volterra first kind of convolution in the scalar and vector cases on the semi-infinite interval. Under the enough of the nature restrictions on the kernel of the integral equation of Volterra operator (the kernel has bounded support), the solution is restored by the right side of the equation, the latter is defined on the infinite part semi-infinite interval. Uniqueness theorems are proved, necessary and sufficient conditions for solvability are found, explicit formulas for solutions are received.
Keywords: Volterra integral equation of the first kind of convolution, the system of equations, the necessary and sufficient conditions for solvability
Mots-clés : an explicit formula. 
@article{SEMR_2012_9_a29,
     author = {A. F. Voronin},
     title = {Recovery solutions of the {Volterra} equation of the first kind of convolution on the half with incomplete data},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {464--471},
     publisher = {mathdoc},
     volume = {9},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2012_9_a29/}
}
TY  - JOUR
AU  - A. F. Voronin
TI  - Recovery solutions of the Volterra equation of the first kind of convolution on the half with incomplete data
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2012
SP  - 464
EP  - 471
VL  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2012_9_a29/
LA  - ru
ID  - SEMR_2012_9_a29
ER  - 
%0 Journal Article
%A A. F. Voronin
%T Recovery solutions of the Volterra equation of the first kind of convolution on the half with incomplete data
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2012
%P 464-471
%V 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2012_9_a29/
%G ru
%F SEMR_2012_9_a29
A. F. Voronin. Recovery solutions of the Volterra equation of the first kind of convolution on the half with incomplete data. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 464-471. http://geodesic.mathdoc.fr/item/SEMR_2012_9_a29/

[1] S.G. Samko, A.A. Kilbas, O.I. Marichev, Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhnika, Moskva, 1987

[2] E.Ch. Titchmarsh, Vvedenie v teoriyu integralov Fure, KomKniga, Moskva, 2007

[3] A.F. Voronin, “Sistema uravnenii Volterra pervogo roda v svertkakh na konechnom intervale”, Differentsalnye uravneniya, 37:9 (2001), 1258–1264 | MR | Zbl

[4] A.F. Voronin, “Obobschenie teoremy Titchmarsha o nositelyakh v svertke na mnogomernye sistemy uravnenii Volterra pervogo roda v svertkakh”, Differentsialnye uravneniya, 39:3 (2003), 416–417 | MR | Zbl

[5] M.G. Krein, “Integralnye uravneniya na polupryamoi s yadrom, zavisyaschim ot raznosti argumentov”, Uspekhi mat. nauk, 13:5 (1958), 3–120 | MR | Zbl

[6] F.D. Gakhov, Yu.I. Cherskii, Uravneniya tipa svertki, Nauka, Moskva, 1978