An extension theorem for slice monogenic functions and some of its consequences |
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Authors: | Fabrizio Colombo Irene Sabadini Daniele C Struppa |
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Institution: | 1.Politecnico di Milano,Dipartimento di Matematica,Milano,Italy;2.Department of Mathematics and Computer Sciences,Schmid College of Science Chapman University,Orange,USA |
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Abstract: | Slice monogenic functions were introduced by the authors in 6]. The central result of this paper is an extension theorem, which shows that every holomorphic function defined on a suitable
domain D of a complex plane can be uniquely extended to a slice monogenic function defined on a domain U
D
, determined by D, in a Euclidean space of appropriate dimension. Two important consequences of the result are a structure theorem for the
zero set of a slice monogenic function (with a related corollary for polynomials with coefficients in Clifford algebras),
and the possibility to construct a multiplicative theory for such functions. Slice monogenic functions have a very important
application in the definition of a functional calculus for n-tuples of noncommuting operators. |
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Keywords: | |
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