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Noncommutative Cauchy Integral Formula

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38123, Trento, Italy

    Riccardo Ghiloni & Alessandro Perotti

  2. Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin, Italy

    Vincenzo Recupero

Authors
  1. Riccardo Ghiloni
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  2. Alessandro Perotti
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  3. Vincenzo Recupero
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Corresponding author

Correspondence to Alessandro Perotti.

Additional information

Communicated by Irene Sabadini.

R. Ghiloni and A. Perotti are partially supported by FIRB 2012 “Differential Geometry and Geometric Function Theory”, MIUR Project “Proprietà geometriche delle varietà reali e complesse” and GNSAGA of INdAM. V. Recupero is a member of GNAMPA of INdAM.

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Ghiloni, R., Perotti, A. & Recupero, V. Noncommutative Cauchy Integral Formula. Complex Anal. Oper. Theory 11, 289–306 (2017). https://doi.org/10.1007/s11785-016-0543-6

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  • DOI: https://doi.org/10.1007/s11785-016-0543-6

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