On Function Theory in Quantum Disc: A q-Analogue of Berezin Transform

TL;DR

This paper proves a theorem demonstrating that the Berezin method can be used to generate a one-parameter deformation of the quantum disc, advancing the understanding of function theory in quantum geometry.

Contribution

It provides a proof of a key theorem showing the applicability of the Berezin method to quantum disc deformations, extending quantum function theory.

Findings

Confirmed the Berezin method's applicability to quantum disc deformations

Established a one-parameter deformation framework for quantum discs

Enhanced mathematical tools for quantum geometry analysis

Abstract

This work contains a proof of theorem 7.3 from math.QA/9808015. This theorem demonstrates the Berezin method to be applicable for producing a well known one-parameter deformation of the quantum disc.