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On the Algebra Generated by Singular Integral Operators with Piecewise Continuous Coefficients

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Toeplitz Centennial

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 4))

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Abstract

The elements of the closed operator algebra ∑p (Γρ) generated by singular integral operators with piecewise continuous coefficients on a closed piecewise Ljapunov contour can be written as the sum of a singular integral operator, countably many generalized Mellin convolutions, and a compact operator. The relation between the symbols of Gohberg-Krupnik and of Duduchava-Dynin is explained by means of a connection between local Fourier and Mellin transforms.

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References

  1. Costabel, M.: Singular integral operators on curves with corners, Integral Equations Oper. Theory 3(1980), 323–349.

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  2. Costabel, M.: An inverse for the Gohberg-Krupnik symbol map, Royal Soc. Edinburgh Proc. 87A(1980), 153–165.

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  3. Duduchava, R.: On bisingular integral operators with discontinuous coefficients, Math. USSR-Sb. 30(1976),515–537.

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  4. Duduchava, R.: On integral operators of convolution type with discontinuous coefficients (russian), Math. Nachr. 79(1977), 75–98.

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  5. Duduchava, R.: Integral Equations with Fixed Singularities. Leipzig, B.G. Teubner 1979.

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  6. Gohberg, I.C. and Krupnik, N. Ja.: Singular integral operators with piecewise continuous coefficients and their symbols, Math. USSR-Izv. 5 (1971), 955–979.

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  7. Michlin, S.G. and Prößdorf, S.: Singuläre Integraloperatoren. Berlin, Akademie-Verlag 1980.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Wegelerstr. 10, 5300, Bonn, W.-Germany

    Martin Costabel

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  1. Martin Costabel
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Editors and Affiliations

  1. School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Israel

    I. Gohberg

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© 1982 Springer Basel AG

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Costabel, M. (1982). On the Algebra Generated by Singular Integral Operators with Piecewise Continuous Coefficients. In: Gohberg, I. (eds) Toeplitz Centennial. Operator Theory: Advances and Applications, vol 4. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5183-1_12

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  • DOI: https://doi.org/10.1007/978-3-0348-5183-1_12

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5184-8

  • Online ISBN: 978-3-0348-5183-1

  • eBook Packages: Springer Book Archive

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