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The Morera Problem in Clifford Algebras and the Heisenberg Group

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Clifford Algebras

Part of the book series: Progress in Mathematical Physics ((PMP,volume 34))

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Abstract

In an open subset Ω of the complex plane ℂ the Morera theorem gives a simple looking necessary and sufficient condition for a continuous function f to be holomorphic in Ω. Namely the vanishing of all the integrals ∫γ f(z) dz, where γ is an arbitrary Jordan curve in Ω whose interior also lies in Ω. The Morera problem consists in finding relatively small families Γ of Jordan curves such that the vanishing of the corresponding integrals still ensures that the conclusion of Morera’s theorem still holds. In this lecture we discuss a number of recent results obtained in the case one considers functions defined in two fairly different settings, the Clifford algebras and the Heisenberg group.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    Carlos A. Berenstein

  2. Department of Mathematics, Georgetown University, 20057, Washington, DC, USA

    Der-Chen Chang

  3. Department of Mathematics, 255 Hurley Building, Notre Dame, IN, 46556, USA

    Wayne M. Eby

  4. Department of Mathematics, Temple University, Philadelphia, PA, 19122, USA

    Wayne M. Eby

Authors
  1. Carlos A. Berenstein
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  2. Der-Chen Chang
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  3. Wayne M. Eby
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Tennessee Technological University, 5054, TN 38505, Cookeville, USA

    Rafał Abłamowicz

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© 2004 Birkhäuser Boston

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Berenstein, C.A., Chang, DC., Eby, W.M. (2004). The Morera Problem in Clifford Algebras and the Heisenberg Group. In: Abłamowicz, R. (eds) Clifford Algebras. Progress in Mathematical Physics, vol 34. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2044-2_1

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  • DOI: https://doi.org/10.1007/978-1-4612-2044-2_1

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3525-1

  • Online ISBN: 978-1-4612-2044-2

  • eBook Packages: Springer Book Archive

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