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arXiv · 1803.00377

Measures that define a compact Cauchy transform

Carmelo Puliatti
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Abstract

The aim of this work is to provide a geometric characterization of the positive Radon measures $\mu$ with compact support on the plane such that the associated Cauchy transform defines a compact operator from $L^2(\mu)$ to $L^2(\mu).$ It turns out that a crucial role is played by the density of the measure and by its Menger curvature.

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Carmelo Puliatti. 2018-03-01. Measures that define a compact Cauchy transform. https://arxiv.org/abs/1803.00377

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