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Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 5, Pages 936–961 (Mi izv1326)  

This article is cited in 2 scientific papers (total in 2 papers)

One-dimensional singular integral equations with coefficients vanishing on countable sets

V. B. Dybin


Abstract: On the basis of the principle of normalization of linear operators a general method is constructed for investigating one-dimensional singular integral equations in the space $L_p(\Gamma,\rho)$ in the case when their coefficients are degenerate on countable sets. In particular, zero sets satisfying the Carleson $\delta$-condition are studied, along with the images of such sets under linear fractional transformations.
Bibliography: 38 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1988, 31:2, 245–271

Bibliographic databases:

UDC: 517.948
MSC: Primary 45E05, 45E10; Secondary 47A53, 30E05, 30D50
Received: 10.10.1985

Citation: V. B. Dybin, “One-dimensional singular integral equations with coefficients vanishing on countable sets”, Izv. Akad. Nauk SSSR Ser. Mat., 51:5 (1987), 936–961; Math. USSR-Izv., 31:2 (1988), 245–271

Citation in format AMSBIB
\Bibitem{Dyb87}
\by V.~B.~Dybin
\paper One-dimensional singular integral equations with coefficients vanishing on countable sets
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 5
\pages 936--961
\mathnet{http://mi.mathnet.ru/izv1326}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=925089}
\zmath{https://zbmath.org/?q=an:0678.45001|0633.45001}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 31
\issue 2
\pages 245--271
\crossref{https://doi.org/10.1070/IM1988v031n02ABEH001068}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Dybin V.B., “Uravnenie svërtki na veschestvennoi pryamoi v prostranstve funktsii, summiruemykh s eksponentsialnymi vesami. chast 1”, Vestnik rossiiskogo universiteta druzhby narodov. seriya: matematika, informatika, fizika, 2011, no. 2, 16–27  elib
    2. V. B. Dybin, S. B. Dzhirgalova, “Scalar Discrete Convolutions in Spaces of Sequences Summed with Exponential Weights—Part 1: One-Sided Invertibility”, Integr. Equ. Oper. Theory, 2014  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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