Basic aspects of symplectic Clifford analysis for the symplectic Dirac operator

Hendrik De Bie; Marie Holíková; Petr Somberg

Basic aspects of symplectic Clifford analysis for the symplectic Dirac operator

Symplectic Geometry 2016-05-24 v2

Authors: Hendrik De Bie , Marie Holíková , Petr Somberg

Abstract

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.

Keywords

symplectic Clifford analysis symplectic Dirac operator symplectic vector space symmetry operators Clifford-Fourier transform reproducing kernel symplectic monogenics

Cite

@article{arxiv.1511.04189,
  title  = {Basic aspects of symplectic Clifford analysis for the symplectic Dirac operator},
  author = {Hendrik De Bie and Marie Holíková and Petr Somberg},
  journal= {arXiv preprint arXiv:1511.04189},
  year   = {2016}
}

Comments

28 pages, various small changes

Basic aspects of symplectic Clifford analysis for the symplectic Dirac operator

Abstract

Keywords

Cite

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