Quaternionic metamonogenic functions in the unit disk
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916424789786624 |
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| author | Morais, J. Porter, R. Michael |
| author_facet | Morais, J. Porter, R. Michael |
| contents | We construct a set of quaternionic metamonogenic functions (that is, in $\mbox{Ker}(D+λ)$ for diverse $λ$) in the unit disk, such that every metamonogenic function is approximable in the quaternionic Hilbert module $L^2$ of the disk. The set is orthogonal except for the small subspace of elements of orders zero and one. These functions are used to express time-dependent solutions of the imaginary-time wave equation in the polar coordinate system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_02117 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quaternionic metamonogenic functions in the unit disk Morais, J. Porter, R. Michael Complex Variables 30G35 (Primary) 42C30, 35J05, 35Q41 (Secondary) We construct a set of quaternionic metamonogenic functions (that is, in $\mbox{Ker}(D+λ)$ for diverse $λ$) in the unit disk, such that every metamonogenic function is approximable in the quaternionic Hilbert module $L^2$ of the disk. The set is orthogonal except for the small subspace of elements of orders zero and one. These functions are used to express time-dependent solutions of the imaginary-time wave equation in the polar coordinate system. |
| title | Quaternionic metamonogenic functions in the unit disk |
| topic | Complex Variables 30G35 (Primary) 42C30, 35J05, 35Q41 (Secondary) |
| url | https://arxiv.org/abs/2203.02117 |