Constructing $3$-Dimensional Monogenic Homogeneous Functions
Analysis of PDEs
2024-06-10 v1
Abstract
This paper is dedicated to the construction of multidimensional spherical monogenics. Firstly, we investigate the construction of monogenic functions in dimension by applying the Dirac operator to the orthonormal bases of spherical harmonics, resulting in orthogonal spherical monogenics. Additionally, we employ the reproducing kernel for monogenic functions and a specialized optimization method to derive various types of -dimensional spherical harmonics and spherical monogenics.
Keywords
Cite
@article{arxiv.2406.04863,
title = {Constructing $3$-Dimensional Monogenic Homogeneous Functions},
author = {Hamed Baghal Ghaffari and Jeffrey A. Hogan and Joseph D. Lakey},
journal= {arXiv preprint arXiv:2406.04863},
year = {2024}
}