Quantization on Nilpotent Lie Groups

By Veronique Fischer, Michael Ruzhansky. 2016

366 citations recorded by the source corpus.

Preface.- Introduction.- Notation and conventions.- 1 Preliminaries on Lie groups.- 2 Quantization on compact Lie groups.- 3 Homogeneous Lie groups.- 4 Rockland operators and Sobolev spaces.- 5 Quantization on graded Lie groups.- 6 Pseudo-differential operators on the Heisenberg group.- A Miscellaneous.- B Group C* and von Neumann algebras.- Schrodinger representations and Weyl quantization.- Explicit symbolic calculus on the Heisenberg group.- List of quantizations.- Bibliography.- Index.

Subfields: Mathematical Physics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/5f1bd482430034ac6c1f730334a1fe66123d26b5

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Citations in the corpus

Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups (2017, background): “[12,14] for the Lie algebra point of view): Definition 2.”
On horizontal Hardy, Rellich, Caffarelli–Kohn–Nirenberg and p-sub-Laplacian inequalities on stratified groups (2016, background): “[21] for discussions from the Lie algebra point of view.”
Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups (2016, result): “For the general background details on homogeneous groups we refer to the book [FS82] by Folland and Stein as well as to the recent monograph [FR16] by V.”
$L^{p}$ -BOUNDS FOR PSEUDO-DIFFERENTIAL OPERATORS ON COMPACT LIE GROUPS (2016, background): “We refer to [FR16] for further explanations and examples of this (nilpotent) setting.”
Nonharmonic Analysis of Boundary Value Problems (2015, background): “The latter approach has further, still “harmonic” extensions, for example, for the global analysis of pseudo-differential operators on the Heisenberg group [26], graded Lie groups [24, 25, 27], or general type I locally compact groups [39].”
$$L^p$$-Bounds for Pseudo-differential Operators on Graded Lie Groups (2019, methodology): “ groups, the Lp-boundedness of the global pseudodiﬀerential calculus for the classes Sm ρ,δ(G× Gb) have been investigated by the third author and V. Fischer with the Caldero´n-Vaillancourt theorem in [29] regardingthe L2(G)-boundedness foroperators with symbol in the class S0 ρ,ρ(G×Gb), and the Lp-b”