Monogenic functions over real alternative *-algebras: the several hypercomplex variables case

Abstract

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 $\ast$-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 $\ast$-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.

22 pages

References in corpus (5)

• Slice regular functions on real alternative algebras
• Cauchy-Riemann operators and local slice analysis over real alternative algebras
• Bochner-Martinelli formula in superspace
• A unified theory of regular functions of a hypercomplex variable
• Generalized partial-slice monogenic functions: the octonionic case