Noncommutative Cauchy Integral Formula
Copyright policy )Noncommutative Cauchy Integral Formula
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"
- Polytechnic University of Turin Italy
- University of Trento Italy
slice regular functions, Functions of hypercomplex variables and generalized variables, Mathematics - Complex Variables, Cauchy integral formula; Functions of a hypercomplex variable; Quaternions; Octonions; Clifford algebras, FOS: Mathematics, Cauchy integral formula, Complex Variables (math.CV), Cauchy integral formula, Functions of a hypercomplex variable, Quaternions, Octonions, Clifford algebras, 30C15, 30G35, 32A30, 17D05
slice regular functions, Functions of hypercomplex variables and generalized variables, Mathematics - Complex Variables, Cauchy integral formula; Functions of a hypercomplex variable; Quaternions; Octonions; Clifford algebras, FOS: Mathematics, Cauchy integral formula, Complex Variables (math.CV), Cauchy integral formula, Functions of a hypercomplex variable, Quaternions, Octonions, Clifford algebras, 30C15, 30G35, 32A30, 17D05
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