Archivio Istituzionale della RicercaThe aim of this paper is to provide and prove the most general Cauchy integral formula for slice regular functions and for continuously differentiable 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.
Noncommutative Cauchy integral formula / Riccardo Ghiloni, Alessandro Perotti; Recupero, Vincenzo. - In: COMPLEX ANALYSIS AND OPERATOR THEORY. - ISSN 1661-8254. - STAMPA. - 11:2(2017), pp. 289-306. [10.1007/s11785-016-0543-6]
Noncommutative Cauchy integral formula
RECUPERO, VINCENZO
2017
Abstract
The aim of this paper is to provide and prove the most general Cauchy integral formula for slice regular functions and for continuously differentiable 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.
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https://hdl.handle.net/11583/2630901
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