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Distributional Solutions of Singular Integral Equations

In: Singular Integral Equations

Author

Listed:
  • Ricardo Estrada

    (Universidad de Costa Rica, Escuela de Matemática)

  • Ram P. Kanwal

    (Penn State University, Department of Mathematics)

Abstract

In this chapter we study the distributional solutions of singular integral equations. The distributional framework is rather convenient for the study of several singular operators, including the singular integrals that we have studied in the previous chapters. Therefore, the study of singular integral equations in spaces of distributions is a natural and important subject. Interestingly, however, the interpretation of singular integrals at the end-points is not straightforward, and so the study of singular integral equations in spaces of distributions over finite intervals turns out to be somewhat difficult.

Suggested Citation

  • Ricardo Estrada & Ram P. Kanwal, 2000. "Distributional Solutions of Singular Integral Equations," Springer Books, in: Singular Integral Equations, chapter 5, pages 175-249, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1382-6_5
    DOI: 10.1007/978-1-4612-1382-6_5
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    Cited by:

    1. A. V. Balakrishnan & M. A. Shubov, 2008. "Reduction of Boundary Value Problem to Possio Integral Equation in Theoretical Aeroelasticity," Journal of Applied Mathematics, John Wiley & Sons, vol. 2008(1).
    2. Qinghua Wu, 2014. "The Approximate Solution of Fredholm Integral Equations with Oscillatory Trigonometric Kernels," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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