Pseudo-differential operators, Wigner transform and Weyl systems on type I locally compact groups
- Author
- Mark Mantoiu and Michael Ruzhansky (UGent)
- Organization
- Abstract
- Let G be a unimodular type I second countable locally compact group and let (G) over cap be its unitary dual. We introduce and study a global pseudo-differential calculus for operator-valued symbols defined on G x (G) over cap, 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.
- Keywords
- locally compact group, nilpotent Lie group, non-commutative Plancherel theorem, pseudo-differential operator, C*-algebra, dynamical system
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8585444
- MLA
- Mantoiu, Mark, and Michael Ruzhansky. “Pseudo-Differential Operators, Wigner Transform and Weyl Systems on Type I Locally Compact Groups.” DOCUMENTA MATHEMATICA, vol. 22, 2017, pp. 1539–92.
- APA
- Mantoiu, M., & Ruzhansky, M. (2017). Pseudo-differential operators, Wigner transform and Weyl systems on type I locally compact groups. DOCUMENTA MATHEMATICA, 22, 1539–1592.
- Chicago author-date
- Mantoiu, Mark, and Michael Ruzhansky. 2017. “Pseudo-Differential Operators, Wigner Transform and Weyl Systems on Type I Locally Compact Groups.” DOCUMENTA MATHEMATICA 22: 1539–92.
- Chicago author-date (all authors)
- Mantoiu, Mark, and Michael Ruzhansky. 2017. “Pseudo-Differential Operators, Wigner Transform and Weyl Systems on Type I Locally Compact Groups.” DOCUMENTA MATHEMATICA 22: 1539–1592.
- Vancouver
- 1.Mantoiu M, Ruzhansky M. Pseudo-differential operators, Wigner transform and Weyl systems on type I locally compact groups. DOCUMENTA MATHEMATICA. 2017;22:1539–92.
- IEEE
- [1]M. Mantoiu and M. Ruzhansky, “Pseudo-differential operators, Wigner transform and Weyl systems on type I locally compact groups,” DOCUMENTA MATHEMATICA, vol. 22, pp. 1539–1592, 2017.
@article{8585444,
abstract = {{Let G be a unimodular type I second countable locally compact group and let (G) over cap be its unitary dual. We introduce and study a global pseudo-differential calculus for operator-valued symbols defined on G x (G) over cap, 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.}},
author = {{Mantoiu, Mark and Ruzhansky, Michael}},
issn = {{1431-0643}},
journal = {{DOCUMENTA MATHEMATICA}},
keywords = {{locally compact group,nilpotent Lie group,non-commutative Plancherel theorem,pseudo-differential operator,C*-algebra,dynamical system}},
language = {{eng}},
pages = {{1539--1592}},
title = {{Pseudo-differential operators, Wigner transform and Weyl systems on type I locally compact groups}},
url = {{https://www.math.uni-bielefeld.de/documenta/vol-22/48.html}},
volume = {{22}},
year = {{2017}},
}