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 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}
}