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 Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 4, Pages 940–964 (Mi izv2086)

Singular integral operators with piecewise continuous coefficients and their symbols

I. Ts. Gokhberg, N. Ya. Krupnik

Abstract: The algebra generated by one-dimensional singular integral operators with piecewise continuous coefficients is studied. Operators acting on the space $L_p$ with a weight are considered. The contour is assumed to consist of closed and open arcs. The structure of the symbols of the operators considered is elucidated. It is found that the symbol is a matrix-function of the second order depending both on $p$ and on the weight. Criteria that the operator be Fredholm and a formula for its index are established.

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:4, 955–979

Bibliographic databases:

UDC: 517.94
MSC: Primary 45E05, 45F05; Secondary 46L20, 47B30, 47G05

Citation: I. Ts. Gokhberg, N. Ya. Krupnik, “Singular integral operators with piecewise continuous coefficients and their symbols”, Izv. Akad. Nauk SSSR Ser. Mat., 35:4 (1971), 940–964; Math. USSR-Izv., 5:4 (1971), 955–979

Citation in format AMSBIB
\Bibitem{GokKru71} \by I.~Ts.~Gokhberg, N.~Ya.~Krupnik \paper Singular integral operators with piecewise continuous coefficients and their symbols \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1971 \vol 35 \issue 4 \pages 940--964 \mathnet{http://mi.mathnet.ru/izv2086} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=291893} \zmath{https://zbmath.org/?q=an:0235.47025} \transl \jour Math. USSR-Izv. \yr 1971 \vol 5 \issue 4 \pages 955--979 \crossref{https://doi.org/10.1070/IM1971v005n04ABEH001127} 

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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
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6. Martin Costabel, “Singular integral operators on curves with corners”, Integr equ oper theory, 3:3 (1980), 323
7. N. Ya. Krupnik, “A sufficient set of $n$-dimensional representations of a Banach algebra and the $n$-symbol”, Funct. Anal. Appl., 14:1 (1980), 50–52
8. Yu. I. Karlovich, V. G. Kravchenko, “Systems of singular integral equations with a shift”, Math. USSR-Sb., 44:1 (1983), 75–95
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20. Karlovich A.Yu., “Singular Integral Operators on Variable Lebesgue Spaces with Radial Oscillating Weights”, Operator Algebras, Operator Theory and Applications, Operator Theory Advances and Applications, 195, 2010, 185–212
21. Karlovich A.Yu., “Singular Integral Operators on Variable Lebesgue Spaces over Arbitrary Carleson Curves”, Topics in Operator Theory: Operators, Matrices and Analytic Functions, Operator Theory Advances and Applications, 1, 2010, 321–336
22. 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
23. A. G. Kamalian, I. M. Spitkovsky, “On the Fredholm Property of a Class of Convolution-Type Operators”, Math. Notes, 104:3 (2018), 404–416
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