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Zbl 0682.45001
Yan, Y.; Sloan, I.H.
On integral equations of the first kind with logarithmic kernels. (English)
[J] J. Integral Equations Appl. 1, No.4, 549-579 (1988). ISSN 0897-3962

The authors give a detailed study on the existence and uniqueness of the solution for one-dimensional integral equations of the first kind with logarithmic kernels. The analysis is given for both closed and open contours, and existence and uniqueness theorems are established. The method of proof is based on the transfinite diameter or logarithmic capacity, and on function spaces associated with Fourier series expansions. The behavior of the solutions is also investigated for the case of polygonal contour, by means of a perturbation argument applied to the results for smooth closed curves.
[J.Burbea]

MSC 2000:: *45E10 Integral equations of the convolution type

Keywords: integral equations of the first kind; logarithmic kernels; transfinite diameter; logarithmic capacity; Fourier series expansions

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