Geodesic
Pseudo-Differential Operators, Wigner Transform and Weyl Systems on Type I Locally Compact Groups
Documenta mathematica, Tome 22 (2017), pp. 1539-1592
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Let G be a unimodular type I second countable locally compact group and let G^ be its unitary dual. We introduce and study a global pseudo-differential calculus for operator-valued symbols defined on G×G^, 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.
DOI : 10.4171/dm/604
Classification : 22D10, 22D25, 47G30
Mots-clés : locally compact group, noncommutative Plancherel theorem 
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     author = {Marius M\u{a}ntoiu and Michael Ruzhansky},
     title = {Pseudo-Differential {Operators,} {Wigner} {Transform} and {Weyl} {Systems} on {Type} {I} {Locally} {Compact} {Groups}},
     journal = {Documenta mathematica},
     pages = {1539--1592},
     year = {2017},
     volume = {22},
     doi = {10.4171/dm/604},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/604/}
}
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Marius Măntoiu; Michael Ruzhansky. Pseudo-Differential Operators, Wigner Transform and Weyl Systems on Type I Locally Compact Groups. Documenta mathematica, Tome 22 (2017), pp. 1539-1592. doi: 10.4171/dm/604

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