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Inversion of the Cauchy integral taken over the double periodic line. (English) Zbl 1055.45003

The author considers in a Hölder type space the following singular integral equation \[ \int_L {u(t)\over u(t- z)}\,dt= f(z);\quad z\in L, \] where \(L\) is a disconnected double periodic line in the complex plane.
Necessary and sufficient conditions for the solvability of the equation and an effective solution are given.

MSC:

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