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Mathematics of the USSR-Izvestiya, 1971, Volume 5, Issue 4, Pages 955–979
DOI: https://doi.org/10.1070/IM1971v005n04ABEH001127 (Mi im2086) 		 
This article is cited in 39 scientific papers (total in 39 papers)

Singular integral operators with piecewise continuous coefficients and their symbols

I. Ts. Gokhberg, N. Ya. Krupnik
English version PDF (1084 kB) Citations (39)
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DOI: https://doi.org/10.1070/IM1971v005n04ABEH001127
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.
Received: 16.06.1970
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1971, Volume 35, Issue 4, Pages 940–964
Bibliographic databases:
UDC: 517.94
MSC: Primary 45E05, 45F05; Secondary 46L20, 47B30, 47G05
Language: English
Original paper language: Russian
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/im2086}
\mathscinet{http://mathscinet.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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    • This publication is cited in the following 39 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:567
    Russian version PDF:195
    English version PDF:7
    References:66
    First page:1
     
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