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Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 2, Pages 388–412 (Mi izv2116)  

This article is cited in 4 scientific papers (total in 4 papers)

Convolution integral operators on a quadrant with discontinuous symbols

R. V. Duduchava


Abstract: Necessary and sufficient conditions are obtained for convolution integral operators on a quadrant with discontinuous symbols to be Noetherian in $L_p$-spaces and in Sobolev–Slobodeckii spaces. The algebra generated by these operators is studied, and a regularizer is constructed in the case of continuity of the symbol.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:2, 371–392

Bibliographic databases:

UDC: 517.9
MSC: Primary 47G05, 47B30; Secondary 45E10
Received: 26.02.1975

Citation: R. V. Duduchava, “Convolution integral operators on a quadrant with discontinuous symbols”, Izv. Akad. Nauk SSSR Ser. Mat., 40:2 (1976), 388–412; Math. USSR-Izv., 10:2 (1976), 371–392

Citation in format AMSBIB
\Bibitem{Dud76}
\by R.~V.~Duduchava
\paper Convolution integral operators on a~quadrant with discontinuous symbols
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 2
\pages 388--412
\mathnet{http://mi.mathnet.ru/izv2116}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=412875}
\zmath{https://zbmath.org/?q=an:0329.47015}
\transl
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 2
\pages 371--392
\crossref{https://doi.org/10.1070/IM1976v010n02ABEH001699}


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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. R. V. Duduchava, “On bisingular integral operators with discontinuous coefficients”, Math. USSR-Sb., 30:4 (1976), 515–537  mathnet  crossref  mathscinet  zmath  isi
    2. R. V. Duduchava, “Discrete convolution operators on the quarter plane and their indices”, Math. USSR-Izv., 11:5 (1977), 1072–1084  mathnet  crossref  mathscinet  zmath
    3. L. I. Sazonov, “$C^*$-algebras of bisingular operators with discontinuous coefficients”, Izv. Math., 63:2 (1999), 367–399  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. R. Duduchava, F.-O. Speck, “Pseudodifferential Operators on Compact Manifolds with Lipschitz Boundary”, Math. Nachr, 160:1 (2009), 149  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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