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

DOI10.25537/dm.2017v22.1539-1592zbMath1403.22006arXiv1506.05854MaRDI QIDQ683770

Michael Ruzhansky, Marius Măntoiu

Publication date: 9 February 2018

Published in: Documenta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.05854

zbMATH Keywords

locally compact groupnoncommutative Plancherel theorem

Mathematics Subject Classification ID

(C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Unitary representations of locally compact groups (22D10) Pseudodifferential operators (47G30)

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Cites Work

• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quantization on nilpotent Lie groups
• The Gohberg lemma, compactness, and essential spectrum of operators on compact Lie groups
• Gevrey functions and ultradistributions on compact Lie groups and homogeneous spaces
• On Fréchet-Hilbert algebras
• Kernel and symbol criteria for Schatten classes and \(r\)-nuclearity on compact manifolds
• Hörmander class of pseudo-differential operators on compact Lie groups and global hypoellipticity
• Intrinsic pseudo-differential calculi on any compact Lie group
• Symbol calculus of square-integrable operator-valued maps
• Parametrix constructions for right invariant differential operators on nilpotent groups
• Quantization of pseudo-differential operators on the torus
• Invertibility of convolution operators on homogeneous groups groups
• The Melin calculus for general homogeneous groups
• Compactness in translation invariant Banach spaces of distributions and compact multipliers
• Pseudodifferential operators on groups with dilations
• On the regular representation of a nonunimodular locally compact group
• Matrix coefficients and a Weyl correspondence for nilpotent Lie groups
• Abstract harmonic analysis of continuous wavelet transforms
• Global functional calculus for operators on compact Lie groups
• Quantizations on nilpotent Lie groups and algebras having flat coadjoint orbits
• A pseudo-differential calculus on the Heisenberg group
• Compactness criteria in Banach spaces in the setting of continuous frames
• \(L^p\)-nuclearity, traces, and Grothendieck-Lidskii formula on compact Lie groups
• Eine Charakterisierung diskreter Gruppen vom Typ I
• Compactness properties of sets of operators and their adjoints
• Noncommutative microlocal analysis. I
• Pseudo-Differential Operators and Symmetries
• Essential spectrum and Fredholm properties for operators on locally compact groups
• Global Quantization of Pseudo-Differential Operators on Compact Lie Groups, SU(2), 3-sphere, and Homogeneous Spaces
• A Pseudo-differential Calculus on Graded Nilpotent Lie Groups
• Distributions sur un groupe localement compact et applications à l'étude des représentations des groupes $p$-adiques
• Totally Bounded Sets of Precompact Linear Operators

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