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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.04863 |
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| _version_ | 1866913381497176064 |
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| author | Ghaffari, Hamed Baghal Hogan, Jeffrey A. Lakey, Joseph D. |
| author_facet | Ghaffari, Hamed Baghal Hogan, Jeffrey A. Lakey, Joseph D. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04863 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constructing $3$-Dimensional Monogenic Homogeneous Functions Ghaffari, Hamed Baghal Hogan, Jeffrey A. Lakey, Joseph D. Analysis of PDEs 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. |
| title | Constructing $3$-Dimensional Monogenic Homogeneous Functions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.04863 |