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arXiv · 2207.13160

Real algebraic geometry of real algebraic Jordan curves in the plane and the Bergman kernel

Steven R. Bell
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Abstract

We characterize the space of restrictions of real rational functions to certain algebraic Jordan curves in the plane via the Dirichlet-to-Neumann map associated to the domain in the complex plane bounded by the curve and its Bergman kernel. The characterization leads to a partial fractions-like decomposition for such rational functions and new ways to describe such Jordan curves. The multiply connected case is also explored.

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Steven R. Bell. 2022-07-26. Real algebraic geometry of real algebraic Jordan curves in the plane and the Bergman kernel. https://arxiv.org/abs/2207.13160

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