Slice regular functions in several variables

Abstract

In this paper, we lay the foundations of the theory of slice regular functions in several variables ranging in any real alternative ${}^{\ast }$-algebra, including quaternions, octonions and Clifford algebras. This theory is an extension of the classical theory of holomorphic functions in several complex variables.

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• A new approach to slice analysis via slice topology
• Almansi-type decomposition for slice regular functions of several quaternionic variables
• Quaternionic slice regularity beyond slice domains
• A unified theory of regular functions of a hypercomplex variable
• A manifold Fueter-Sce phenomenon in one hypercomplex variable
• On the first-order theories of quaternions and octonions