An extension theorem for slice monogenic functions and some of its consequences
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- Colombo, F., Sabadini, I. & Struppa, D.C. Isr. J. Math. (2010) 177: 369. doi:10.1007/s11856-010-0051-8
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Slice monogenic functions were introduced by the authors in . 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 UD, 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.