arXiv subjects

Erik I. Díaz-Ortíz

Publications and source records attributed to Erik I. Díaz-Ortíz.

2 recordsLinked to original sources

arXiv2019

Asymptotic expantion of covariant symbol on the complex unit sphere

Starting from a complete family (not defined by the reproducing kernel) for the unit sphere $\mathbf S^n$ in the complex $n$-space $\mathbb C^n$, we obtain an asymptotic expansion for the associated Berezin transform. The proof involves the computation of the asymptotic behaviour of functions in the complete family. Furthermore, we prove an Egorov-type theorem for the covariant symbol related to a pseudo-differential operator on $L^2(\mathbf S^n)$.

math.CV↗

arXiv2017

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

We describe the symbolic calculus of operators on the unit sphere in the complex n-space $\mathbb C^n$ 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.

math.CA↗