Singular Integral Equations

  • Rainer Kress
Part of the Applied Mathematical Sciences book series (AMS, volume 82)


In this chapter we will consider one-dimensional singular integral equations involving Cauchy principal values that arise from boundary value problems for holomorphic functions. The investigations of these integral equations with Cauchy kernels by Gakhov, Muskhelishvili, Vekua, and others have had a great impact on the further development of the general theory of singular integral equations. For our introduction to integral equations they will provide an application of the general idea of regularizing singular operators as described in Chapter 5. We assume the reader is acquainted with basic complex analysis.


Holomorphic Function Singular Integral Equation Riemann Problem Singular Integral Operator Cauchy Kernel 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Rainer Kress
    • 1
  1. 1.Institut für Numerische und Angewandte MathematikUniversität GöttingenGöttingenGermany

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