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 Izv. Vyssh. Uchebn. Zaved. Mat., 2011, Number 7, Pages 3–12 (Mi ivm7692)

A method for the localization of singularities of a solution to a convolution-type equation of the first kind with a step kernel

A. L. Ageev, T. V. Antonova

Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Scienes, Ekaterinburg, Russia

Abstract: We consider the problem on the localization of singularities (delta-functions) of a solution to a convolution-type equation of the first kind with a step kernel. We propose a new regularization method which allows to calculate the number of singularities and to approximate them. The accuracy of approximation is calculated. We obtain bounds for an important characteristic of the method, namely, the separability threshold. We prove the order-optimality of the proposed method on classes of functions with singularities both with respect to the accuracy and the separability.

Keywords: ill-posed problems, localization of singularities, regularization method, separability threshold.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:7, 1–8

Bibliographic databases:

UDC: 517.988

Citation: A. L. Ageev, T. V. Antonova, “A method for the localization of singularities of a solution to a convolution-type equation of the first kind with a step kernel”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 7, 3–12; Russian Math. (Iz. VUZ), 55:7 (2011), 1–8

Citation in format AMSBIB
\Bibitem{AgeAnt11} \by A.~L.~Ageev, T.~V.~Antonova \paper A method for the localization of singularities of a~solution to a~convolution-type equation of the first kind with a~step kernel \jour Izv. Vyssh. Uchebn. Zaved. Mat. \yr 2011 \issue 7 \pages 3--12 \mathnet{http://mi.mathnet.ru/ivm7692} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2931711} \transl \jour Russian Math. (Iz. VUZ) \yr 2011 \vol 55 \issue 7 \pages 1--8 \crossref{https://doi.org/10.3103/S1066369X11070012} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80051702293}