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arXiv · 1812.00627

Geometric properties of measures related to holomorphic functions having positive imaginary or real part

Annemarie Luger·Mitja Nedic
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Abstract

In this paper, we study the properties of a certain class of Borel measures on $\mathbb{R}^n$ that arise in the integral representation of Herglotz-Nevanlinna functions. In particular, we find that restrictions to certain hyperplanes are of a surprisingly simple form and show that the supports of such measures can not lie within particular geometric regions, e.g. strips with positive slope. Corresponding results are derived for measures on the unit poly-torus with vanishing mixed Fourier coefficients. These measures are closely related to functions mapping the unit polydisk analytically into the right half-plane.

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Annemarie Luger, Mitja Nedic. 2018-12-03. Geometric properties of measures related to holomorphic functions having positive imaginary or real part. https://doi.org/10.1007/s12220-020-00368-4

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