Constructing 3-Dimensional Monogenic Homogeneous Functions
Abstract
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.
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