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Application of the Abstract Approach to Singular Equations on the Real Line with Fractional Linear Shift

In: Equations with Involutive Operators

Author

Listed:
  • Nikolai Karapetiants

    (Rostov State University, Department of Mathematics)

  • Stefan Samko

    (Universidade do Algarve, Faculdade de Ciências e Tecnologia)

Abstract

Let Г = R 1 and let τ(x) be a fractional linear shift on the real line R 1: $$ \tau (x) = \frac{{\delta x + \beta }}{{x - \delta }}$$ satisfying the Carleman condition τ[τ(x)] ≡ x. We consider the following singular integral operator with such a shift: A $$ K\varphi = a(x)\varphi (x) + b(x)\varphi [\tau (x)] + c(x)(S\varphi )(x) + d(x)(S\varphi )[\tau (x)] + T\varphi ,x \in {R^1}, $$ where T is a compact operator (in the space under consideration below).

Suggested Citation

  • Nikolai Karapetiants & Stefan Samko, 2001. "Application of the Abstract Approach to Singular Equations on the Real Line with Fractional Linear Shift," Springer Books, in: Equations with Involutive Operators, chapter 6, pages 275-338, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0183-0_6
    DOI: 10.1007/978-1-4612-0183-0_6
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