Noncommutative Cauchy Integral Formula

作者：Ghiloni Riccardo; Perotti Alessandro^*; Recupero Vincenzo

来源：Complex Analysis and Operator Theory, 2017, 11(2): 289-306.

DOI：10.1007/s11785-016-0543-6

• Cauchy integral formula
• Functions of a hypercomplex variable
• Quaternions
• Octonions
• Clifford algebras

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.

• 出版日期2017-2