Symplectic inverse spectral theory for pseudodifferential operators

DOI10.1007/978-0-8176-8244-6_13zbMath1277.47065arXiv0808.2862OpenAlexW2143002051MaRDI QIDQ2914660

San Vũ Ngoc

Publication date: 20 September 2012

Published in: Progress in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0808.2862

zbMATH Keywords

semiclassical spectrumBohr-Sommerfeld rulesmicrolocal analysisinverse spectral theoryprincipal symbolsemiclassical pseudodifferential operatorssemiclassical spectral asymptoticssymplectic classification

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Pseudodifferential operators (47G30)

Related Items (9)

Spectral asymptotics of semiclassical unitary operators ⋮ Semiclassical quantization and spectral limits of ħ-pseudodifferential and Berezin-Toeplitz operators ⋮ Symplectic invariants of semitoric systems and the inverse problem for quantum systems ⋮ Quantum footprints of Liouville integrable systems ⋮ Integrable systems, symmetries, and quantization ⋮ Semiclassical inverse spectral theory for singularities of focus-focus type ⋮ Asymptotic lattices, good labellings, and the rotation number for quantum integrable systems ⋮ Spectral invariants for coupled spin-oscillators ⋮ Inverse spectral theory for semiclassical Jaynes-Cummings systems

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