Advances in Applied Clifford Algebras

, Volume 27, Issue 2, pp 1103–1132 | Cite as

Basic Aspects of Symplectic Clifford Analysis for the Symplectic Dirac Operator

  • Hendrik De BieEmail author
  • Marie Holíková
  • Petr Somberg


In the present article we study basic aspects of the symplectic version of Clifford analysis associated to the symplectic Dirac operator. Focusing mostly on the symplectic vector space of real dimension 2, this involves the analysis of first order symmetry operators, symplectic Clifford-Fourier transform, reproducing kernel for the symplectic Fischer product and the construction of bases of symplectic monogenics for the symplectic Dirac operator.


Symplectic Dirac operator Symplectic spinors Symmetry operators Reproducing kernel Fischer product Bases of symplectic monogenics 

Mathematics Subject Classification

Primary 53C27 Secondary 53D05 81R25 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Hendrik De Bie
    • 1
    Email author
  • Marie Holíková
    • 2
  • Petr Somberg
    • 3
  1. 1.Department of Mathematical Analysis, Faculty of Engineering and ArchitectureGhent UniversityGentBelgium
  2. 2.Department of Mathematics and Mathematical Education, Faculty of EducationCharles UniversityPraha 1Czech Republic
  3. 3.Mathematical Institute of Charles UniversityPraha 8-KarlínCzech Republic

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