Pseudo-differential operators, Wigner transform and Weyl systems on type I locally compact groups

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Title: Pseudo-differential operators, Wigner transform and Weyl systems on type I locally compact groups
Authors: Mantoiu, M
Ruzhansky, M
Item Type: Journal Article
Abstract: Let G be a unimodular type I second countable locally compact group and let Gb be its unitary dual. We introduce and study a global pseudo-differential calculus for operator-valued symbols defined on G × Gb , and its relations to suitably defined Wigner transforms and Weyl systems. We also unveil its connections with crossed products C ∗ -algebras associated to certain C ∗ -dynamical systems, and apply it to the spectral analysis of covariant families of operators. Applications are given to nilpotent Lie groups, in which case we relate quantizations with operator-valued and scalar-valued symbols.
Issue Date: 13-Dec-2017
Date of Acceptance: 29-May-2017
ISSN: 1431-0635
Publisher: Universität Bielefeld
Start Page: 1539
End Page: 1592
Journal / Book Title: Documenta Mathematica
Volume: 22
Copyright Statement: ©The Authors
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Funder's Grant Number: EP/K039407/1
Keywords: locally compact group
nilpotent Lie group
noncommutative Plancherel theorem
pseudo-differential operator
C ∗ -algebra
dynamical system
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences

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