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The Fueter mapping theorem in integral form and the ℱ-functional calculus

✍ Scribed by Fabrizio Colombo; Irene Sabadini; Frank Sommen

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
254 KB
Volume
33
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Communicated by K. Guerlebeck

In this paper we show a version of the Fueter mapping theorem that can be stated in integral form based on the Cauchy formulas for slice monogenic (or slice regular) functions. More precisely, given a holomorphic function f of a paravector variable, we generate a monogenic function f by an integral transform whose kernel is particularly simple. This procedure allows us to define a functional calculus for n-tuples of commuting operators (called F-functional calculus) based on a new notion of spectrum, called F-spectrum, for the n-tuples of operators. Analogous results are shown for the quaternionic version of the theory and for the related F-functional calculus.

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