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

Hannes Wendt (U Oslo)

May 08. 2025, 16:15 — 16:45

A fundamental lemma in Werner's foundational work on quantum harmonic analysis concerns the integrability of operator-operator convolutions. This notion has recently been adapted to a setting where the operator-shift is implemented by a unitary representation of the affine group by Berge, Berge, Luef and Skrettingland. We propose a setup where the shifts are encoded by a locally compact group action on a semifinite von Neumann algebra. We generalise the orthogonality relations for matrix coefficients of square-integrable representations, proved by Duflo and Moore for locally compact groups, to a theorem that leads to the integrability of the von Neumann operator convolution. In the case of a commutative von Neumann algebra, the theorem reduces to Young's convolution inequality.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Quantum Harmonic Analysis (Workshop)
Organizer(s):
Markus Faulhuber (U of Vienna)
Hans G. Feichtinger (U of Vienna)
Franz Luef (NTNU, Trondheim)