Pseudo-Differential Operators, Wigner Transform and Weyl Systems on Type I Locally Compact Groups
Marius MantoiuDept. de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Las Palmeras 3425, Santiago, Chile
Michael RuzhanskyDepartment of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, United Kingdom
Let be a unimodular type I second countable locally compact group and let be its unitary dual. We introduce and study a global pseudo-differential calculus for operator-valued symbols defined on , and its relations to suitably defined Wigner transforms and Weyl systems. We also unveil its connections with crossed products -algebras associated to certain -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.
Cite this article
Marius Mantoiu, Michael Ruzhansky, Pseudo-Differential Operators, Wigner Transform and Weyl Systems on Type I Locally Compact Groups. Doc. Math. 22 (2017), pp. 1539–1592DOI 10.4171/DM/604