Measures that define a compact Cauchy transform

Puliatti, Carmelo

doi:10.1090/proc/14419

Measures that define a compact Cauchy transform
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by Carmelo Puliatti

Proc. Amer. Math. Soc. 147 (2019), 2069-2080

DOI: https://doi.org/10.1090/proc/14419

Published electronically: January 29, 2019

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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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Measures that define a compact Cauchy transform
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Abstract: