On Function Theory in Quantum Disc: Invariant Kernels

TL;DR

This paper develops a method to prove the invariance of kernels of integral operators in the context of function theory in the quantum disc, building on previous work on integral representations.

Contribution

It introduces a new method to establish kernel invariance, advancing the understanding of integral operators in quantum function theory.

Findings

Proved invariance of integral kernels in quantum disc

Connected kernel invariance to integral representations

Extended previous results on quantum function theory

Abstract

In our earlier work math.QA/9808015 some results on integral representations of functions in quantum disc were announced. It was then shown in math.QA/9808037 that the validity of those results is related to the invariance of kernels of some integral operators. We introduce here a method which allows us to prove the invariance of the above kernels.