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Two-term Equations (A + QB)ϕ = f with an Involutive Operator Q; an Abstract Approach and Applications

  • Nikolai Karapetiants
  • Stefan Samko

Abstract

In Sections 11–12 we presented an approach to the investigation of Fredholmness of singular integral equations with Carleman shift on a closed or open curve in the case of continuous coefficients. This approach is also applicable to many other types of equations, because it, in fact, gives some general scheme of the investigation of Fredholmness of operators, containing an involutive operator Q, that is, an operator such that Q 2 = I, or, more generally, Q n = I. This approach may be applicable, in particular, to
  1. a)

    convolution equations with reflection;

     
  2. b)

    discrete convolutions with oscillating coefficients;

     
  3. c)

    singular integral equations with Carleman shift on the axis R1, when the shift function is unbounded;

     
  4. d)

    singular integral equations with Carleman shift in the case of piecewise continuous coefficients, etc.

     

Keywords

Compact Operator Singular Integral Equation Singular Integral Operator Fredholm Operator Abstract Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Nikolai Karapetiants
    • 1
  • Stefan Samko
    • 2
  1. 1.Department of MathematicsRostov State UniversityRostov-na-DonuRussia
  2. 2.Faculdade de Ciências e TecnologiaUniversidade do AlgarveFaroPortugal

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