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

Nikolai Karapetiants and Stefan Samko
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Nikolai Karapetiants: Rostov State University, Department of Mathematics
Stefan Samko: Universidade do Algarve, Faculdade de Ciências e Tecnologia

Chapter 6 in Equations with Involutive Operators, 2001, pp 275-338 from Springer

Abstract: 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).

Keywords: Compact Operator; Matrix Operator; Singular Integral Equation; Weighted Space; Singular Integral Operator (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-1-4612-0183-0_6

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