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Slice monogenic functions
No full textAbstract. In this paper we offer a new definition of monogenicity for functions defined on R^{n+1} with values in the Clifford
algebra R_n following an idea inspired by a recent paper by Gentili and Struppa.
This new class of monogenic functions contains the polynomials (and, more in general, power series) with coefficients in the
Clifford algebra R_n. We will prove a Cauchy integral
formula as well as some of its consequences. Finally, we deal with the zeroes of some polynomials and power series
Noncommutative Functional Calculus. Theory and Applications of Slice Hyperholomorphic Functions
No full text
An extension theorem for slice monogenic functions and some of its consequences
No full textAbstract. Slice monogenic functions were introduced by the authors in a paper appeared in Israel J. Math. in 2009. 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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