A Structure Formula for Slice Monogenic Functions and Some of its Consequences
In this paper we show a structure formula for slice monogenic functions (see Lemma 2.2 and  for further details): we will show that this formula is a key tool to prove several results, among which we mention the Cauchy integral formula with slice monogenic kernel. This Cauchy formula allows us to extend the validity of the functional calculus for n-tuples of noncommuting operators introduced in . In this wider setting, most of the properties which hold for the Riesz-Dunford functional calculus of a single operator, such as the Spectral Mapping Theorem and the Spectral Radius Theorem, still hold.
KeywordsSlice monogenic functions slice monogenic kernel structure formula for slice monogenic functions functional calculus for n-tuples of linear operators
Mathematics Subject Classification (2000)Primary 30G35 Secondary 47A10
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