Quaternionic Regularity via Analytic Functional Calculus

Florian-Horia Vasilescu

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arXiv · 1905.13051

Quaternionic Regularity via Analytic Functional Calculus

Florian-Horia Vasilescu

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Abstract

Denoting by $\mathbb{M}$ the complexification of the quaternionic algebra $\mathbb{H}$, we characterize the family of those $\mathbb{M}$-valued functions, defined on subsets of $\H$, whose values are actually quaternions, using an intrinsic approach. In particular, we show that the slice quaternionic regularity can be characterized via a Cauchy type transform acting on the space of analytic $\mathbb{M}$-valued stem functions.

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Florian-Horia Vasilescu. 2019-05-29. Quaternionic Regularity via Analytic Functional Calculus. https://arxiv.org/abs/1905.13051

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