The metaplectic representation, Weyl operators and spectral theory

DOI10.1016/0022-1236(81)90042-2zbMath0469.58017OpenAlexW4249627698MaRDI QIDQ1157062

Shlomo Sternberg, Victor W. Guillemin

Publication date: 1981

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(81)90042-2

zbMATH Keywords

spectral theorymetaplectic representationWeyl operatorspseudo-differential operatorsasymptotic growth of eigenvaluesbundle of negative half-formsChazarain- Duistermaat-Guillemin trace formulaGrassmannian of Lagrangian subspacesHelton clustering theorem

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Pseudodifferential and Fourier integral operators on manifolds (58J40) Other representations of locally compact groups (22D12) Pseudodifferential operators and other generalizations of partial differential operators (35S99)

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Cites Work

• Eigenvalue distribution theorems for certain homogeneous spaces
• Sur le spectre des opérateurs elliptiques à bicaracteristiques toutes périodiques
• Geometric quantization and multiplicities of group representations
• Smooth functions invariant under the action of a compact Lie group
• Asymptotics of eigenvalue clusters for the Laplacian plus a potential
• Formule de Poisson pour les variétés riemanniennes
• Pseudo differential operators
• The spectral function of an elliptic operator
• Sur certains groupes d'opérateurs unitaires
• Fourier integral operators. I
• Fourier integral operators. II
• Some Problems in Integral Geometry and Some Related Problems in Micro-Local Analysis
• The Spectral Theory of Toeplitz Operators. (AM-99)
• ON ASYMPTOTIC DISTRIBUTION OF EIGENVALUES OF PSEUDODIFFERENTIAL OPERATORS IN $ \mathbf R^n$
• The weyl calculus of pseudo-differential operators
• Pseudo‐differential operators
• The de Sitter groupL 4,1 and the bound states of hydrogen atom
• Linear Symmetries of Free Boson Fields
• Regularization of kepler's problem and the averaging method on a manifold
• Quantization and unitary representations
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