Slice regular functions on real alternative algebras |
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Authors: | R. Ghiloni A. Perotti |
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Affiliation: | Department of Mathematics, University of Trento, Via Sommarive 14, I-38123 Povo-Trento, Italy |
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Abstract: | In this paper we develop a theory of slice regular functions on a real alternative algebra A. Our approach is based on a well-known Fueter's construction. Two recent function theories can be included in our general theory: the one of slice regular functions of a quaternionic or octonionic variable and the theory of slice monogenic functions of a Clifford variable. Our approach permits to extend the range of these function theories and to obtain new results. In particular, we get a strong form of the fundamental theorem of algebra for an ample class of polynomials with coefficients in A and we prove a Cauchy integral formula for slice functions of class C1. |
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Keywords: | MSC: 30C15 30G35 32A30 17D05 |
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