Abstract
We expose the main results of a theory of slice regular functions on a real alternative algebra A, based on a well-known Fueter construction. Our general theory includes the theory of slice regular functions of a quaternionic or octonionic variable and the theory of slice monogenic functions of a Clifford variable. Our approach permits us to extend the range of these function theories and to obtain new results. In particular, we show that a fundamental theorem of algebra with multiplicities holds for an ample class of polynomials with coefficients in A. We give several examples to illustrate some interesting aspects of the theory.
Mathematics Subject Classification (2010). Primary 30C15; Secondary 30G35, 32A30.
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© 2011 Springer Basel AG
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Ghiloni, R., Perotti, A. (2011). A New Approach to Slice Regularity on Real Algebras. In: Sabadini, I., Sommen, F. (eds) Hypercomplex Analysis and Applications. Trends in Mathematics. Springer, Basel. https://doi.org/10.1007/978-3-0346-0246-4_8
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DOI: https://doi.org/10.1007/978-3-0346-0246-4_8
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Publisher Name: Springer, Basel
Print ISBN: 978-3-0346-0245-7
Online ISBN: 978-3-0346-0246-4
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