Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774677 | Journal of Mathematical Analysis and Applications | 2018 | 18 Pages |
Abstract
We present a theory of ultradistributional boundary values for harmonic functions defined on the Euclidean unit ball. We also give a characterization of ultradifferentiable functions and ultradistributions on the sphere in terms of their spherical harmonic expansions. To this end, we obtain explicit estimates for partial derivatives of spherical harmonics, which are of independent interest and refine earlier estimates by Calderón and Zygmund. We apply our results to characterize the support of ultradistributions on the sphere via Abel summability of their spherical harmonic expansions.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
ÄorÄe VuÄkoviÄ, Jasson Vindas,