Dimensional estimates for measures on quaternionic spheres

Dimensional estimates for measures on quaternionic spheres

In this article we provide lower bounds for the lower Hausdorff dimension of finite measures assuming certain restrictions on their quaternionic spherical harmonics expansions. This estimate is an analog of a result previously obtained by the authors for the complex spheres.

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Veröffentlicht in:Journal of mathematical analysis and applications 2024-01, Vol.529 (2), p.127281, Article 127281
Hauptverfasser: Ayoush, Rami, Wojciechowski, Michał
Format: Artikel
Sprache:eng
Schlagworte:
Hausdorff dimension
Quaternionic spheres
Spherical harmonics
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Zusammenfassung:In this article we provide lower bounds for the lower Hausdorff dimension of finite measures assuming certain restrictions on their quaternionic spherical harmonics expansions. This estimate is an analog of a result previously obtained by the authors for the complex spheres.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127281