This article is cited in 1 paper

Real, complex and functional analysis

Research of a threshold (correlation) method and application for localization of singularities

D. V. Kurlikovskii, A. L. Ageev, T. V. Antonova

Institute of Mathematics and Mechanics, ul. S. Kovalevskoi, 16, 620990, Ekaterinburg, Russia

Abstract: The localization of singularities for functions of one ($\delta$-functions and discontinuities of the first kind) and two (line of discontinuity) dimensions is discussed. General scheme of the study of this ill-posed problems is presented. Using this scheme new problems of localization of singularities are investigated.

Keywords: ill-posed problems, discontinuities of the first kind, line of discontinuity, localization of singularities, regularizing method, separation threshold.

UDC: 517.988.68

MSC: 65J20

Received December 29, 2015, published October 7, 2016

DOI: 10.17377/semi.2016.13.066

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