Abstract
In this paper we introduce an alternative way of defining the curvilinear Cauchy integral over non-rectifiable arcs on the complex plane. We construct this integral as the convolution of the distribution (2πiz)-1 with a certain distribution such that its support is a non-rectifiable arc. These convolutions are called Cauchy transforms. As an application, solvability conditions of the Riemann boundary value problem are derived under very weak conditions on the boundary.
Mathematics Subject Classification (2000). Primary 30E25; secondary 30E20.
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Kats, B.A. (2012). The Riemann Boundary Value Problem on Non-rectifiable Arcs and the Cauchy Transform. In: Arendt, W., Ball, J., Behrndt, J., Förster, KH., Mehrmann, V., Trunk, C. (eds) Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Operator Theory: Advances and Applications, vol 221. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0297-0_24
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DOI: https://doi.org/10.1007/978-3-0348-0297-0_24
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