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Complex Analysis and Operator Theory

, Volume 6, Issue 2, pp 341–357 | Cite as

Duality for Hermitean Systems in \({\mathbb R^{2n}}\)

  • Ricardo Abreu-BlayaEmail author
  • Juan Bory-Reyes
  • Richard Delanghe
  • Frank Sommen
Article

Abstract

In this paper, using the ring structure of the space of circulant (2 × 2)-matrix, we characterize the dual of the (Fréchet) space of germs of left Hermitean monogenic matrix functions in a compact set \({{\bf E}\subset\mathbb R^{2n}}\). As an application we describe the dual space of the so-called h-monogenic functions satisfying simultaneously two Dirac type equations.

Keywords

Hermitean Clifford analysis Duality theory 

Mathematics Subject Classification (2000)

30G35 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • Ricardo Abreu-Blaya
    • 1
    Email author
  • Juan Bory-Reyes
    • 2
  • Richard Delanghe
    • 3
  • Frank Sommen
    • 3
  1. 1.Departamento de MatemáticaUniversidad de HolguínHolguínCuba
  2. 2.Departamento de MatemáticaUniversidad de OrienteSantiago de CubaCuba
  3. 3.Department of Mathematical Analysis, Faculty of EngineeringGhent UniversityGentBelgium

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