2024/06/07 by Ghaffari, Hamed Baghal, Hogan, Jeffrey A., Lakey, Joseph D.
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2406.04863
This paper is dedicated to the construction of multidimensional spherical monogenics. Firstly, we investigate the construction of monogenic functions in dimension 3 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 3-dimensional spherical harmonics and spherical monogenics.