A Duflo-Moore theorem for ergodic group actions on semifinite von Neumann algebras

TL;DR

This paper generalizes the Duflo-Moore theorem to ergodic, trace-preserving group actions on semifinite von Neumann algebras, establishing new orthogonality relations and convolution inequalities.

Contribution

It extends the Duflo-Moore theorem to a broader setting involving ergodic group actions on semifinite von Neumann algebras, introducing new convolution inequalities.

Findings

Generalized orthogonality relations for ergodic group actions

Established convolution inequalities extending Young's inequality

Unified framework for quantum harmonic analysis

Abstract

We prove a generalization of the orthogonality relations of Duflo and Moore for ergodic, trace-preserving group actions on von Neumann algebras that are integrable in a suitable sense. We also obtain convolution inequalities that generalize both Young's inequality for convolution on locally compact groups and inequalities for operator-operator convolutions in Werner's quantum harmonic analysis.