Noncommutative Cauchy integral formula

Abstract

The aim of this paper is to provide and prove the most general Cauchy integral formula for slice regular functions and for C^1 functions on a real alternative *-algebra. Slice regular functions represent a generalization of the classical concept of holomorphic function of a complex variable in the noncommutative and nonassociative settings. As an application, we obtain two kinds of local series expansion for slice regular functions.

13 pages, an example has been added at the end of Section 4. To appear in "Complex Analysis and Operator Theory"

References in corpus (2)

• A new series expansion for slice regular functions
• Power and spherical series over real alternative *-algebras