Dimensions of Riesz products and pluriharmonic measures
Evgueni Doubtsov
TL;DR
This paper investigates the energy and Hausdorff dimensions of Riesz products on the unit sphere in complex space and extends similar results to pluriharmonic measures on the torus, providing new insights into their geometric properties.
Contribution
It offers new estimates for the energy and Hausdorff dimensions of Riesz products and pluriharmonic measures, advancing understanding of their geometric and measure-theoretic characteristics.
Findings
Derived bounds for energy and Hausdorff dimensions of Riesz products
Extended results to pluriharmonic measures on the torus
Provided new estimates for geometric properties of these measures
Abstract
We estimate the energy and Hausdorff dimensions of the Riesz products on the unit sphere of , . Also, we obtain similar results for the pluriharmonic measures on the torus.
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Taxonomy
TopicsFunctional Equations Stability Results · Analytic and geometric function theory · Mathematical Analysis and Transform Methods