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Clifford Analysis on the Space of Vectors, Bivectors and ℓ-vectors

  • Irene Sabadini
  • Frank Sommen
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

In this paper we propose several extensions of Clifford analysis. First, we recall the most important definitions and properties for the usual Dirac operator, i.e. the operator defined for functions of a vector variable, and we discuss the importance of using differential forms. Next we discuss Clifford analysis in several vector variables and in particular so called “symplicial monogenics”, that are related to the representation theory of Spin(m). Then we study several canonically defined Clifford algebras valued systems of differential equations defined on the space of bivectors, for which we provide a rather complete theory, and more in general on the space of ℓ-vectors.

Mathematics Subject Classification (2000)

30G35 

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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • Irene Sabadini
    • 1
  • Frank Sommen
    • 2
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2.Department of Mathematical AnalysisState University of GhentGentBelgium

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