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

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

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 a) convolution equations with reflection; b) discrete convolutions with oscillating coefficients; c) singular integral equations with Carleman shift on the axis R1, when the shift function is unbounded; d) singular integral equations with Carleman shift in the case of piecewise continuous coefficients, etc.

Suggested Citation

  • Nikolai Karapetiants & Stefan Samko, 2001. "Two-term Equations (A + QB)ϕ = f with an Involutive Operator Q; an Abstract Approach and Applications," Springer Books, in: Equations with Involutive Operators, chapter 4, pages 153-222, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0183-0_4
    DOI: 10.1007/978-1-4612-0183-0_4
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