Wigner transform and pseudodifferential operators on symmetric spaces of non-compact type

TL;DR

This paper develops a general framework for the Wigner transform and pseudodifferential operators on symmetric spaces of non-compact type, extending classical analysis tools to these geometric settings.

Contribution

It introduces a comprehensive expression for the Wigner transform and explores the Weyl calculus in the context of non-compact symmetric spaces, a novel extension of existing theory.

Findings

Derived a general formula for the Wigner transform on symmetric spaces

Analyzed the Weyl calculus of pseudodifferential operators in this setting

Extended classical analysis tools to non-compact symmetric spaces

Abstract

We obtain a general expression for a Wigner transform (Wigner function) on symmetric spaces of non-compact type and study the Weyl calculus of pseudodifferential operators on them.