Algebras with general commutation relations and their applications. I: Pseudodifferential equations with increasing coefficients

DOI10.1007/BF01083678zbMath0482.58028OpenAlexW2028028077MaRDI QIDQ1162745

V. P. Maslov, Vladimir E. Nazaikinskii

Publication date: 1979

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01083678

zbMATH Keywords

asymptotic solutionssemiclassical approximationgraded Lie algebrasLie algebrasHamiltonian operatorpseudo-differential equationnonlinear commutation relationsasymptotics of the Cauchy problemexistence of a right quasi inverselinear operator as a function of a collection of simpler operators which do not commuteordered quantisationregular representation for commutation relationssymbols of the regular representation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Pseudodifferential operators as generalizations of partial differential operators (35S05) Functional calculus for linear operators (47A60) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Pseudodifferential and Fourier integral operators on manifolds (58J40) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items (3)

New insight into the partition theory of integers related to problems of thermodynamics and mesoscopic physics ⋮ New formulas for Maslov's canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics ⋮ Algebra of symmetries of three-frequency hyperbolic resonance

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