A Positive Quantization on Type I Locally Compact Groups

TL;DR

This paper introduces a positive Berezin-type quantization framework for unimodular type I locally compact groups, utilizing operator-valued symbols on the dual and the group, inspired by recent pseudo-differential calculus advancements.

Contribution

It develops a novel positive quantization method for a broad class of groups, extending pseudo-differential calculus techniques to operator-valued symbols on the dual and the group.

Findings

Constructed a Berezin-type quantization for unimodular type I groups

Extended pseudo-differential calculus to operator-valued symbols

Provided a framework for positive quantization on locally compact groups

Abstract

Let $\G$ be a unimodular type I second countable locally compact group and $\wG$ its unitary dual. Motivated by a recent pseudo-differential calculus, we develop a positive Berezin-type quantization with operator-valued symbols defined on $\wG\times\G$.