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 Sib. Zh. Ind. Mat., 2014, Volume 17, Number 2, Pages 32–40 (Mi sjim830)

Reconstruction of the convolution operator from the right-hand side on the real half-axis

A. F. Voronin

Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk

Abstract: We study a Volterra integral equation of the first kind in convolutions on a semi-infinite interval. Under rather natural constraints on the kernel and the right-hand side of a Volterra integral equation (the kernel has bounded support and the support of the right-hand side may be unbounded), it is possible to reconstruct the integral operator of the equation (the solution and the kernel of the integral operator) from the right-hand side of the equation. Some uniqueness theorem is proved, as well as necessary and sufficient conditions for solvability and the explicit formulas for the solution and the kernel are obtained.

Keywords: Volterra integral equation of the first kind, convolution, uniqueness, reconstruction formula for the convolution operator.

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English version:
Journal of Applied and Industrial Mathematics, 2014, 8:3, 428–435

Bibliographic databases:

UDC: 517.968.22

Citation: A. F. Voronin, “Reconstruction of the convolution operator from the right-hand side on the real half-axis”, Sib. Zh. Ind. Mat., 17:2 (2014), 32–40; J. Appl. Industr. Math., 8:3 (2014), 428–435

Citation in format AMSBIB
\Bibitem{Vor14} \by A.~F.~Voronin \paper Reconstruction of the convolution operator from the right-hand side on the real half-axis \jour Sib. Zh. Ind. Mat. \yr 2014 \vol 17 \issue 2 \pages 32--40 \mathnet{http://mi.mathnet.ru/sjim830} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3379237} \transl \jour J. Appl. Industr. Math. \yr 2014 \vol 8 \issue 3 \pages 428--435 \crossref{https://doi.org/10.1134/S1990478914030168} 

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This publication is cited in the following articles:
1. Voronin A.F., “Reconstruction of a Convolution Operator From the Right-Hand Side on the Semiaxis”, J. Inverse Ill-Posed Probl., 23:5 (2015), 543–550
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