Constructing $3$-Dimensional Monogenic Homogeneous Functions
Constructing $3$-Dimensional Monogenic Homogeneous Functions
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 …