Monogenic functions over real alternative *-algebras: fundamental results and applications

Qinghai Huo; Guangbin Ren; Zhenghua Xu

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arXiv · 2504.01359

Monogenic functions over real alternative *-algebras: fundamental results and applications

Qinghai Huo·Guangbin Ren·Zhenghua Xu

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Abstract

The concept of monogenic functions over real alternative $\ast$-algebras has recently been introduced to unify several classical monogenic (or regular) functions theories in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. This paper explores the fundamental properties of these monogenic functions, focusing on the Cauchy-Pompeiu integral formula and Taylor series expansion in hypercomplex subspaces, among which the non-commutativity and especially non-associativity of multiplications demand full considerations. The theory presented herein provides a robust framework for understanding monogenic functions in the context of real alternative $\ast$-algebras, shedding light on the interplay between algebraic structures and hypercomplex analysis.

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Qinghai Huo, Guangbin Ren, Zhenghua Xu. 2025-04-02. Monogenic functions over real alternative *-algebras: fundamental results and applications. https://arxiv.org/abs/2504.01359

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