Geodesic
Localization of discontinuities of the first kind methods for the solution of a convolution-type equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2014), pp. 72-76 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a convolution-type equation of the first kind from $L_1$ to $L_1$. We construct and investigate regularizing methods for localization (detection of positions) of discontinuities of the first kind of solution to this equation. Under additional conditions of exact solution, we obtain estimates for the accuracy of localization and for the separability threshold, which are another important characteristics of the methods.
Keywords: ill-posed problem, localization of singularities, regularizing method, separation threshold. 
@article{IVM_2014_3_a6,
     author = {D. V. Kurlikovskii},
     title = {Localization of discontinuities of the first kind methods for the solution of a~convolution-type equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {72--76},
     year = {2014},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_3_a6/}
}
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D. V. Kurlikovskii. Localization of discontinuities of the first kind methods for the solution of a convolution-type equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2014), pp. 72-76. http://geodesic.mathdoc.fr/item/IVM_2014_3_a6/

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