Spectral and regularity properties of a pseudo-differential calculus related to Landau quantization
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Publication:601086
DOI10.1007/s11868-010-0001-6zbMath1200.81061arXiv0810.3874OpenAlexW2006086647MaRDI QIDQ601086
Franz Luef, Maurice A. De Gosson
Publication date: 3 November 2010
Published in: Journal of Pseudo-Differential Operators and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0810.3874
Pseudodifferential operators as generalizations of partial differential operators (35S05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Commutation relations and statistics as related to quantum mechanics (general) (81S05)
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The Schrödinger kernel of the twisted Laplacian and cyclic models ⋮ Quantum mechanics in phase space: the Schrödinger and the Moyal representations ⋮ Coherent states quantization for generalized Bargmann spaces with formulae for their attached Berezin transforms in terms of the Laplacian on \(\mathbb C^{N }\) ⋮ A symplectic extension map and a new Shubin class of pseudo-differential operators ⋮ A pseudo-differential calculus on non-standard symplectic space; spectral and regularity results in modulation spaces ⋮ Sampling and interpolation in Bargmann-Fock spaces of polyanalytic functions ⋮ Balian-Low type theorems on \(L^2(\mathbb{C})\) ⋮ A pseudodifferential calculus on non-standard symplectic space ⋮ A deformation quantization theory for noncommutative quantum mechanics ⋮ METAPLECTIC FORMULATION OF THE WIGNER TRANSFORM AND APPLICATIONS
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