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A jump problem for \(\beta \)-analytic functions in domains with fractal boundaries. (English) Zbl 1184.30025

Summary: Let \(\gamma \) be a simple closed Jordan curve in the complex plane \(\mathbb C\), let \( \Omega ^{+}\) and \(\Omega ^{ - }\) be the corresponding domains in \(\mathbb C\), with \(0\in \Omega ^{+}\) and \(\infty \in \Omega ^{ - }\). Classes of complex valued functions satisfying some boundary conditions as well as integral representations for them are considered.

MSC:

30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
30E25 Boundary value problems in the complex plane
28A80 Fractals
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