A new approach to slice analysis via slice topology

Abstract

In this paper we summarize some known facts on slice topology in the quaternionic case, and we deepen some of them by proving new results and discussing some examples. We then show, following [18], how this setting allows us to generalize slice analysis to the general case of functions with values in a real left alternative algebra, which includes the case of slice monogenic functions with values in Clifford algebra. Moreover, we further extend slice analysis, in one and several variables, to functions with values in a Euclidean space of even dimension. In this framework, we study the domains of slice regularity, we prove some extension properties and the validity of a Taylor expansion for a slice regular function.

Modified the definition of $\widetilde{P_I}(z,r)$ in 8.2. The Version of Record of this article is published in Adv. Appl. Clifford Algebras, and is available online at https://doi.org/10.1007/s00006-021-01170-3

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• Slice regular functions on real alternative algebras
• Power series and analyticity over the quaternions
• Twistor transforms of quaternionic functions and orthogonal complex structures
• A new series expansion for slice regular functions
• The algebra of slice functions
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Cited by in corpus (1)

• A representation formula for slice regular functions over slice-cones in several variables