Geodesic
Pseudo-Differential Operators, Wigner Transform and Weyl Systems on Type I Locally Compact Groups
Documenta mathematica, Tome 22 (2017), pp. 1539-1592.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Let $\mathsf{G}$ be a unimodular type I second countable locally compact group and let $\hat{\mathsf{G}}$ be its unitary dual. We introduce and study a global pseudo-differential calculus for operator-valued symbols defined on $\mathsf{G}\times\hat{\mathsf{G}}$, and its relations to suitably defined Wigner transforms and Weyl systems. We also unveil its connections with crossed products $C^\ast$-algebras associated to certain $C^\ast$-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.
Classification : 22D10, 22D25, 47G30
Keywords: locally compact group, noncommutative Plancherel theorem 
@article{DOCMA_2017__22__a5,
     author = {Mantoiu, Marius and Ruzhansky, Michael},
     title = {Pseudo-Differential {Operators,} {Wigner} {Transform} and {Weyl} {Systems} on {Type} {I} {Locally} {Compact} {Groups}},
     journal = {Documenta mathematica},
     pages = {1539--1592},
     publisher = {mathdoc},
     volume = {22},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a5/}
}
TY  - JOUR
AU  - Mantoiu, Marius
AU  - Ruzhansky, Michael
TI  - Pseudo-Differential Operators, Wigner Transform and Weyl Systems on Type I Locally Compact Groups
JO  - Documenta mathematica
PY  - 2017
SP  - 1539
EP  - 1592
VL  - 22
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a5/
LA  - en
ID  - DOCMA_2017__22__a5
ER  - 
%0 Journal Article
%A Mantoiu, Marius
%A Ruzhansky, Michael
%T Pseudo-Differential Operators, Wigner Transform and Weyl Systems on Type I Locally Compact Groups
%J Documenta mathematica
%D 2017
%P 1539-1592
%V 22
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a5/
%G en
%F DOCMA_2017__22__a5
Mantoiu, Marius; Ruzhansky, Michael. Pseudo-Differential Operators, Wigner Transform and Weyl Systems on Type I Locally Compact Groups. Documenta mathematica, Tome 22 (2017), pp. 1539-1592. http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a5/