Dimensional estimates for measures on quaternionic spheres
Rami Ayoush, Micha{\l} Wojciechowski
TL;DR
This paper establishes lower bounds on the Hausdorff dimension of measures on quaternionic spheres based on their harmonic expansion properties, extending previous complex sphere results.
Contribution
It introduces new lower bounds for measure dimensions on quaternionic spheres, generalizing earlier complex sphere findings.
Findings
Provides explicit lower bounds for Hausdorff dimension of measures
Extends harmonic analysis techniques from complex to quaternionic spheres
Offers a framework for understanding measure regularity on quaternionic manifolds
Abstract
In this article we provide lower bounds for the lower Hausdorff dimension of finite measures assuming certain restrictions on their quaternionic spherical harmonics expansion. This estimate is an analog of a result previously obtained by the authors for the complex spheres.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Mathematical Modeling in Engineering · Mathematical Dynamics and Fractals