A pseudo-differential calculus on the Heisenberg group

DOI10.1016/J.CRMA.2013.12.006zbMath1287.22002arXiv1402.6615OpenAlexW1965812383MaRDI QIDQ2445184

Michael Ruzhansky, Veronique Fischer

Publication date: 14 April 2014

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.6615

zbMATH Keywords

Heisenberg groupSchrödinger representationhypoellipticitysubellipticsymbol classWeyl quantisationpseudo differential calculus

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Analysis on other specific Lie groups (43A80)

Related Items (17)

Nonlinear damped wave equations for the sub-Laplacian on the Heisenberg group and for Rockland operators on graded Lie groups ⋮ \(L^p\)-bounds for pseudo-differential operators on graded Lie groups ⋮ Spectral summability for the quartic oscillator with applications to the Engel group ⋮ L²-L^p estimates and Hilbert–Schmidt pseudo differential operators on the Heisenberg motion group ⋮ Symbolic calculus and M-ellipticity of pseudo-differential operators on ℤn ⋮ Localization operator and Weyl transform on reduced Heisenberg group with multidimensional center ⋮ \(L^p\)-boundedness of pseudo-differential operators on rank one Riemannian symmetric spaces of noncompact type ⋮ On trace formulae of the generalised heat potential operator ⋮ Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups ⋮ Pseudo-differential operators, Wigner transform and Weyl systems on type I locally compact groups ⋮ Elements of potential theory on Carnot groups ⋮ Trace class and Hilbert-Schmidt pseudo differential operators on step two nilpotent Lie groups ⋮ Quantizations on nilpotent Lie groups and algebras having flat coadjoint orbits ⋮ Hilbert-Schmidt and trace class pseudo-differential operators on the abstract Heisenberg group ⋮ Global and concrete quantizations on general type I groups ⋮ On (λ, μ)-Classes on the Engel Group ⋮ Continuity and compactness for pseudo-differential operators with symbols in quasi-Banach spaces or Hörmander classes

Cites Work

• Quantization on nilpotent Lie groups
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Lower bounds for operators on graded Lie groups
• Phase-space analysis and pseudodifferential calculus on the Heisenberg group
• Noncommutative microlocal analysis. I
• Pseudo-Differential Operators and Symmetries
• 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

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