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arXiv · 2203.02117

Quaternionic metamonogenic functions in the unit disk

J. Morais·R. Michael Porter
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Abstract

We construct a set of quaternionic metamonogenic functions (that is, in $\mbox{Ker}(D+\lambda)$ for diverse $\lambda$) 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.

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J. Morais, R. Michael Porter. 2022-03-04. Quaternionic metamonogenic functions in the unit disk. https://doi.org/10.1007/s40590-023-00557-5

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