English

Berezin symbols of operators on the unit sphere of $\mathbb C^n$

Classical Analysis and ODEs 2017-02-21 v1

Abstract

We describe the symbolic calculus of operators on the unit sphere in the complex n-space Cn\mathbb C^n defined by the Berezin quantization. In particular, we derive a explicit formula for the composition of Berezin symbol and with that a noncommutative star product. In the way is necessary introduce a holomorphic spaces which admit a reproducing kernel in the form of generalized hypergeometric series.

Keywords

Cite

@article{arxiv.1702.05708,
  title  = {Berezin symbols of operators on the unit sphere of $\mathbb C^n$},
  author = {Erik I. Díaz-Ortíz},
  journal= {arXiv preprint arXiv:1702.05708},
  year   = {2017}
}