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Advances in Analysis and Geometry pp 161–185Cite as

Birkhäuser

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

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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.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Via Bonardi, 9, Milano, 20133, Italy

    Irene Sabadini

  2. Department of Mathematical Analysis, State University of Ghent, Galglaan,2, Gent, 9000, Belgium

    Frank Sommen

Authors
  1. Irene Sabadini
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  2. Frank Sommen
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Editor information

Editors and Affiliations

  1. Faculty of Science and Technology, University of Macau, 3001, Macau, China

    Tao Qian

  2. Basel, Switzerland

    Thomas Hempfling

  3. Centre for Mathematics and its Applications Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, Australia

    Alan McIntosh

  4. Department of Mathematical Analysis, University of Ghent, Galglaan 2, Ghent, 9000, Belgium

    Frank Sommen

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© 2004 Springer Basel AG

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Sabadini, I., Sommen, F. (2004). Clifford Analysis on the Space of Vectors, Bivectors and ℓ-vectors. In: Qian, T., Hempfling, T., McIntosh, A., Sommen, F. (eds) Advances in Analysis and Geometry. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7838-8_9

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  • DOI: https://doi.org/10.1007/978-3-0348-7838-8_9

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9589-7

  • Online ISBN: 978-3-0348-7838-8

  • eBook Packages: Springer Book Archive

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