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Mat. Sb. (N.S.), 1976, Volume 101(143), Number 4(12), Pages 584–609 (Mi msb2920)  

This article is cited in 10 scientific papers (total in 10 papers)

On bisingular integral operators with discontinuous coefficients

R. V. Duduchava


Abstract: Necessary and sufficient conditions are obtained for bisingular integral operators on piecewise smooth Lyapunov curves with discontinuous coefficients in the $L_p$-spaces with a weight to be Noetherian. The Banach algebra generated by these operators is studied; a regularizer is constructed in the case of continuous coefficients.
Bibliography: 40 titles.

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English version:
Mathematics of the USSR-Sbornik, 1976, 30:4, 515–537

Bibliographic databases:

UDC: 517.43
MSC: Primary 47G05; Secondary 47B30, 46L20
Received: 26.02.1975

Citation: R. V. Duduchava, “On bisingular integral operators with discontinuous coefficients”, Mat. Sb. (N.S.), 101(143):4(12) (1976), 584–609; Math. USSR-Sb., 30:4 (1976), 515–537

Citation in format AMSBIB
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\by R.~V.~Duduchava
\paper On bisingular integral operators with discontinuous coefficients
\jour Mat. Sb. (N.S.)
\yr 1976
\vol 101(143)
\issue 4(12)
\pages 584--609
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=487595}
\zmath{https://zbmath.org/?q=an:0341.47032}
\transl
\jour Math. USSR-Sb.
\yr 1976
\vol 30
\issue 4
\pages 515--537
\crossref{https://doi.org/10.1070/SM1976v030n04ABEH002286}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1976FU24400006}


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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. A. V. Glebov, V. M. Deundyak, “Homotopic classification of noetherian systems of singular and bisingular integral operators with discontinuous coefficients”, Funct. Anal. Appl., 12:3 (1978), 222–224  mathnet  crossref  mathscinet  zmath
    2. Martin Costabel, “Singular integral operators on curves with corners”, Integr equ oper theory, 3:3 (1980), 323  crossref  mathscinet  zmath
    3. Martin Costabel, “Boundary integral operators on curved polygons”, Annali di Matematica, 133:1 (1983), 305  crossref  mathscinet  zmath  isi
    4. Bottcher A., Silbermann B., “The Finite Section Method for Toeplitz-Operators on the Quarter-Plane with Piecewise Continuous Symbols”, Math. Nachr., 110 (1983), 279–291  crossref  mathscinet  isi
    5. L. I. Sazonov, “Bisingular characteristic operators with discontinuous coefficients in the space $L_2(\mathbf R_2)$”, Funct. Anal. Appl., 19:2 (1985), 158–159  mathnet  crossref  mathscinet  zmath  isi
    6. Pasenchuk A., “On the Noether Theory of Linear Conjugation Operator on the Tore in a Count-Hilbert Space”, 298, no. 1, 1988, 37–40  mathscinet  zmath  isi
    7. Deundyak V., Simonenko I., Stukopin V., “The Index of Families of Noetherian Singular and Bisingular Integral-Operators with Piecewise Continuous Coefficients on Composed Curves”, Dokl. Akad. Nauk, 338:2 (1994), 158–161  mathnet  mathscinet  zmath  isi
    8. R. Duduchava, T. Latsabidze, A. Saginashvili, “Singular integral operators with the complex conjugation on curves with cusps”, Integr equ oper theory, 22:1 (1995), 1  crossref  mathscinet  zmath  isi
    9. L. I. Sazonov, “$C^*$-algebras of bisingular operators with discontinuous coefficients”, Izv. Math., 63:2 (1999), 367–399  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. Martin Costabel, “An inverse for the Gohberg-Krupnik symbol map”, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 87:1-2 (2011), 153  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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