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Subharmonic Configurations and Algebraic Cauchy Transforms of Probability Measures by Björk, Jan-Erik; Borcea, Julius; Bøgvad, Rikard is a scholarly article available to read on EtoBox.

What is Subharmonic Configurations and Algebraic Cauchy Transforms of Probability Measures about?

We study subharmonic functions whose Laplacian is supported on a null set and in connected components of of the complement to the support admit harmonic extensions to larger sets. We prove that if such a function has a piecewise holomorphic derivative, then it is locally piecewise harmonic. In generic cases it coincides locally with the maximum of finitely many harmonic functions. Moreover, we describe the support when the holomorphic derivative satisfies a global algebraic equation. The proofs follow classical patterns and our methods may also be of independent interest.

Author

Björk, Jan-Erik; Borcea, Julius; Bøgvad, Rikard

Published

2009

Language

EN