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The Carleman type singular integral equations. (English) Zbl 0624.45002

The authors consider the Riemann boundary value problem and particular cases of the singular integral equation \[ \alpha (\xi)g(\xi)-\lambda \beta (\xi)\int_{C}\gamma (\omega)g(\omega)/(\omega -\xi)d\omega =f(\xi),\quad \xi \in C, \] without some essential assumptions. Well- known results and many examples are given. [Reviewer’s remark: There are a few inaccuracies in the paper\(\}\).
Reviewer: Z.Binderman

MSC:

45E05 Integral equations with kernels of Cauchy type
30E25 Boundary value problems in the complex plane
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