Ghiloni, Riccardo and Perotti, Alessandro (2012) *Volume Cauchy formulas for slice functions on real associative *-algebras.* UTM; 754 . Trento : Università degli Studi di Trento.

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## Abstract

We introduce a family of Cauchy integral formulas for slice and slice regular functions on a real associative *-algebra. For each suitable choice of a real vector subspace of the algebra, a different formula is given, in which the domains of integration are subsets of the subspace. In particular, in the quaternionic case, we get a volume Cauchy formula. In the Clifford algebra case, the choice of the paravector subspace R^(n+1) gives a volume Cauchy formula for slice monogenic functions.

Item Type: | Departmental Technical Report |
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Publisher policy set phrase: | This is the Author's Original Manuscript of an article whose final and definitive form, the Version of Record, has been published in the Complex Variables and Elliptic Equations [25 Sep 2012] [copyright Taylor & Francis], available online at: http://www.tandfonline.com/10.1080/17476933.2012.709851 |

Department or Research center: | Mathematics |

Subjects: | Q Science > QA Mathematics > QA299.6 Analysis Q Science > QA Mathematics > QA445 Geometry |

Uncontrolled Keywords: | Cauchy integral formula; slice regular functions; quaternions; Clifford algebras |

Additional Information: | AMS Primary 30G35; Secondary 32A30, 30E20, 13J30 |

Repository staff approval on: | 24 Jul 2012 15:54 |

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