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Invariance of the Fredholm radius of an operator in potential theory. (English) Zbl 0657.31004
One of the classical methods of solving the Dirichlet problem in \(R^ n\) is the method of integral equations. Using this method for a non-smooth regions it is useful to know the Fredholm radius of an integral operator playing a role in the method. It is shown in the paper that in the case of a Jordan domain in the plane the Fredholm radius of that operator does not change under the conformal mapping of the boundary.

MSC:
31A25 Boundary value and inverse problems for harmonic functions in two dimensions
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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