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A Structure Formula for Slice Monogenic Functions and Some of its Consequences

  • Fabrizio Colombo
  • Irene Sabadini
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

In this paper we show a structure formula for slice monogenic functions (see Lemma 2.2 and [1] 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 [6]. 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.

Keywords

Slice 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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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Fabrizio Colombo
    • 1
  • Irene Sabadini
    • 1
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly

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