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arXiv · 2309.03698

Generalized partial-slice monogenic functions

Zhenghua Xu·Irene Sabadini
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Abstract

The two function theories of monogenic and of slice monogenic functions have been extensively studied in the literature and were developed independently; the relations between them, e.g. via Fueter mapping and Radon transform, have been studied. The main purpose of this article is to describe a new function theory which includes both of them as special cases. This theory allows to prove nice properties such as the identity theorem, a Representation Formula, the Cauchy (and Cauchy-Pompeiu) integral formula, the maximum modulus principle, a version of the Taylor and Laurent series expansions. As a complement, we shall also offer two approaches to these functions via slice functions and via global differential operators. In addition, we discuss the conformal invariance property under a proper group of M\"{o}bius transformations preserving the partial symmetry of the involved domains.

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Zhenghua Xu, Irene Sabadini. 2023-09-07. Generalized partial-slice monogenic functions. https://doi.org/10.1090/tran%2F9356

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