The existence-uniqueness of the solution and its behaviour for one-dimensional integral equations of the first kind with logarithmic kernels are investigated.The analysis is based on the transfinite diameter or logarithmic capacity and spaces deriving from Fourier series.The uniqueness results apply to any closed bounded subset of the plane.The other results apply to open arcs, polygons and other regions with piecewise-smooth boundaries.
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Yan et al. (1988) studied this question.
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