Khatisashvili, N. Inversion of the Cauchy integral taken over the double periodic line. (English) Zbl 1055.45003 Georgian Math. J. 10, No. 1, 133-144 (2003). 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. Reviewer: Zbigniew Binderman (Warszawa) MSC: 45E05 Integral equations with kernels of Cauchy type 30E25 Boundary value problems in the complex plane Keywords:singular integral equation of Cauchy type; inversion formula; boundary value problem PDFBibTeX XMLCite \textit{N. Khatisashvili}, Georgian Math. J. 10, No. 1, 133--144 (2003; Zbl 1055.45003) Full Text: EuDML