An extension theorem for slice monogenic functions and some of its consequences
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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 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.
- F. Brackx, R. Delanghe and F. Sommen, Clifford Analysis, Pitman Researc h Notes in Mathematics, Vol. 76, 1982.
- F. Colombo and I. Sabadini, A structure formula for slice monogenic functions and some of its consequences, in Hypercomplex Analysis, Trends in Mathematics, Birkhäuser, Basel, 2009, pp. 101–114.
- F. Colombo and I. Sabadini, The Cauchy formula with s-monogenic kernel and a functional calculus for noncommuting operators, preprint, 2008.
- F. Colombo, I. Sabadini and D. C. Struppa, Duality theorems for slice hyperholomorphic functions, Journal für die Reine und Angewandte Mathematik (2010), to appear.
- F. Colombo, G. Gentili, I. Sabadini and D. C. Struppa, A functional calculus in a non commutative setting, Electronic Research Announcements of the American Mathematical Society 14 (2007), 60–68.
- F. Colombo, I. Sabadini and D. C. Struppa, Slice monogenic functions, Israel Journal of Mathematics 171 (2009), 385–403. CrossRef
- F. Colombo, I. Sabadini and D.C. Struppa, A new functional calculus for noncommuting operators, Journal of Functional Analysis 254 (2008), 2255–2274. CrossRef
- F. Colombo, I. Sabadini, F. Sommen and D. C. Struppa, Analysis of Dirac Systems and Computational Algebra, Progress in Mathematical Physics, Vol. 39, Birkhäuser, Boston, 2004.
- T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematics, Vol. 123, Springer-Verlag, New York, 1991.
- An extension theorem for slice monogenic functions and some of its consequences
Israel Journal of Mathematics
Volume 177, Issue 1 , pp 369-389
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- The Hebrew University Magnes Press
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- 1. Politecnico di Milano, Dipartimento di Matematica, Via Bonardi, 9, 20133, Milano, Italy
- 2. Department of Mathematics and Computer Sciences, Schmid College of Science Chapman University, Orange, CA, 92866, USA