Various Representations of Holomorphic Functions by Cauchy and Analogous Integrals

N. I. Muskhelishvili
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N. I. Muskhelishvili: Institute of Mathematics Tiflis

Chapter Chapter 8 in Singular Integral Equations, 1958, pp 187-201 from Springer

Abstract: Abstract One of the most natural methods of solution of various boundary problems involving holomorphic functions consists of expressing the unknown holomorphic function in the form of a Cauchy or analogous integral; this expression, substituted into the boundary condition, reduces to an integral equation. In fact, such a method was used in the last section for the solution of the classical and modified Dirichlet problems.

Keywords: Holomorphic Function; Dirichlet Problem; Homogeneous Equation; Real Constant; Fredholm Equation (search for similar items in EconPapers)
Date: 1958
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DOI: 10.1007/978-94-009-9994-7_8

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