2025/06/10 by Xu, Zhenghua, Ding, Chao, Wang, Haiyan
#32A26 #47G10 #Complex Variables (math.CV) #FOS: Mathematics #Primary: 30G35 #Secondary: 17D05
paper · doi:10.48550/arxiv.2506.08307
The notion of monogenic (or regular) functions, which is a correspondence of holomorphic functions, has been studied extensively in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. Recently, the concept of monogenic functions over real alternative ∗-algebras has been introduced to unify several classical monogenic functions theories. In this paper, we initiate the study of monogenic functions of several hypercomplex variables over real alternative ∗-algebras, which naturally extends the theory of several complex variables to a very general setting. In this new setting, we develop some fundamental properties, such as Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.