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A Note on the Fredholm Theory of Singular Integral Operators with Cauchy and Mellin Kernels, II

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Operator Theory, Functional Analysis and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 282))

Abstract

Necessary and sufficient conditions for the Fredholmness of a class of singular integral operators in weighted L p-spaces on the interval (0, 1) of the real line are formulated under weaker conditions than in Junghanns and Kaiser (Oper Theory Adv Appl 271:291–325, 2018). Moreover, results on the one-sided invertibility of the operators under consideration are proved.

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References

  1. A. Böttcher, I.M. Spitkovsky, Pseudodifferential operators with heavy spectrum. Integr. Equ. Oper. Theory 19, 251–269 (1994)

    Article  MathSciNet  Google Scholar 

  2. R. Duduchava, Integral Equations with Fixed Singularities (BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1979)

    MATH  Google Scholar 

  3. I. Gohberg, N. Krupnik, One-Dimensional Linear Singular Integral Equations. Vol I: Introduction. Operator Theory: Advances and Applications, vol. 53 (Birkhäuser Verlag, Basel, 1992)

    Google Scholar 

  4. P. Junghanns, R. Kaiser, A numerical approach for a special crack problem. Dolomites Res. Notes Approx. 10, 56–67 (2017)

    MathSciNet  MATH  Google Scholar 

  5. P. Junghanns, R. Kaiser, A note on the Fredholm theory of singular integral operators with Cauchy and Mellin kernels, in In Operator Theory, Analysis and the State Space Approach. In Honor of Rien Kaashoek. Operator Theory : Advances and Applications, vol. 271 (Birkhäuser, Basel, 2018), 291–325

    Google Scholar 

  6. S.G. Mikhlin, S. Prössdorf, Singular Integral Operators (Akademie-Verlag, Berlin, 1986)

    Book  Google Scholar 

  7. N.I. Muskhelishvili, Singular Integral Equations. Boundary Problems of Function Theory and Their Application to Mathematical Physics (P. Noordhoff N. V., Groningen, 1953)

    Google Scholar 

  8. R. Schneider, Integral equations with piecewise continuous coefficients in L p-spaces with weight. J. Integr. Equ. 9, 135–152 (1985)

    MathSciNet  MATH  Google Scholar 

  9. E.C. Titchmarsh, Introduction to the Theory of Fourier Integrals, 3rd edn. (Chelsea Publishing Co., New York, 1986)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Chemnitz University of Technology, Faculty of Mathematics, Chemnitz, Germany

    Peter Junghanns

  2. TU Bergakademie Freiberg, Faculty of Mathematics and Computer Science, Freiberg, Germany

    Robert Kaiser

Authors
  1. Peter Junghanns
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  2. Robert Kaiser
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Corresponding author

Correspondence to Peter Junghanns .

Editor information

Editors and Affiliations

  1. Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    M. Amélia Bastos

  2. Departamento de Matemática, Universidade de Aveiro, Aveiro, Portugal

    Luís Castro

  3. Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Lisboa, Portugal

    Alexei Yu. Karlovich

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Junghanns, P., Kaiser, R. (2021). A Note on the Fredholm Theory of Singular Integral Operators with Cauchy and Mellin Kernels, II. In: Bastos, M.A., Castro, L., Karlovich, A.Y. (eds) Operator Theory, Functional Analysis and Applications. Operator Theory: Advances and Applications, vol 282. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-51945-2_18

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