Harmonicity of a function via harmonicity of its spherical means
Analysis of PDEs
2021-10-12 v2
Abstract
It is proved that harmonic functions are characterized by harmonicity of their spherical means, for which purpose the iterated spherical means are used. The similar characterization of solutions to the modified Helmholtz equation (panharmonic functions) is given. Another description of harmonic functions is the pointwise equality of a function and its iterated mean over an admissible pair of spheres.
Keywords
Cite
@article{arxiv.2110.03449,
title = {Harmonicity of a function via harmonicity of its spherical means},
author = {Nikolay Kuznetsov},
journal= {arXiv preprint arXiv:2110.03449},
year = {2021}
}
Comments
4 pages, no figures