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Functional and Singular Integral Equations with Carleman Shifts in the Case of Continuous Coefficients

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 this chapter we begin with properties of generalized Carleman shifts and consider the so-called α(t)-factorization of functions (Section 9). We show how this factorization works when we deal with a functional equation with a degenerate symbol (Section 10). In the final Sections 11 and 12 we present the results on Fredholmness of singular integral equations with Carleman shifts on a closed or open curve in order to reveal the ideas which lead to the abstract approach developed later in Chapter 4.

Suggested Citation

  • Nikolai Karapetiants & Stefan Samko, 2001. "Functional and Singular Integral Equations with Carleman Shifts in the Case of Continuous Coefficients," Springer Books, in: Equations with Involutive Operators, chapter 3, pages 111-152, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0183-0_3
    DOI: 10.1007/978-1-4612-0183-0_3
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