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

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

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
\Bibitem{Dud76} \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 \mathnet{http://mi.mathnet.ru/msb2920} \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
2. Martin Costabel, “Singular integral operators on curves with corners”, Integr equ oper theory, 3:3 (1980), 323
3. Martin Costabel, “Boundary integral operators on curved polygons”, Annali di Matematica, 133:1 (1983), 305
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
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
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
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
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
9. L. I. Sazonov, “$C^*$-algebras of bisingular operators with discontinuous coefficients”, Izv. Math., 63:2 (1999), 367–399
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
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