Algebras with general commutation relations and their applications. II. Unitary-nonlinear operator equations

DOI10.1007/BF01083679zbMath0482.58029MaRDI QIDQ1162746

V. P. Maslov, Mikhail V. Karasev

Publication date: 1979

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

zbMATH Keywords

asymptotic solutionsPoisson bracketCauchy problem for linear problemsEuler-Vlasov equationordered quantisationoscillation densityoscillation frontquasi classical asymptotics of solutionsselfadjoint operators in a Hilbert space satisfying commutation relationsunitary nonlinear equations of Hartree typeVlasov-Liouville equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear elliptic equations (35J60) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Pseudodifferential and Fourier integral operators on manifolds (58J40) Applications of PDEs on manifolds (58J90) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (23)

Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters ⋮ Poisson symmetry algebras and the asymptotics of spectral series ⋮ Semiclassical asymptotics of the spectrum of a two-dimensional Hartree type operator near boundaries of spectral clusters ⋮ Spectral Theory and Representations\\ of Nilpotent Groups ⋮ Quantization of symplectic manifolds with conical points ⋮ Duality of algebras with an involution and generalized shift operators ⋮ Geometry of the transport equation in multicomponent WKB approximations ⋮ Generalized Foldy-Wouthuysen transformation and pseudodifferential operators ⋮ Localized asymptotic solutions of the self-consistent field equation ⋮ Asymptotic solutions to the Hartree equation near a sphere. Asymptotics of self-consistent potentials ⋮ Weyl and ordered calculus of noncommuting operators ⋮ Peierls substitution and the Maslov operator method ⋮ Coherent transform of the spectral problem and algebras with nonlinear commutation relations. ⋮ Semiclassical asymptotic spectrum of the two-dimensional Hartree operator near a local maximum of the eigenvalues in a spectral cluster ⋮ Symbolic calculus on nilpotent Lie groups and applications ⋮ Asymptotics of the spectrum of a two-dimensional Hartree-type operator with a Coulomb self-action potential near the lower boundaries of spectral clusters ⋮ Multicomponent Wentzel–Kramers–Brillouin approximation on arbitrary symplectic manifolds: A star product approach ⋮ Algebra of symmetries of three-frequency hyperbolic resonance ⋮ Symplectic groupoids and Poisson manifolds ⋮ Advances in quantization: quantum tensors, explicit star-products, and restriction to irreducible leaves ⋮ On the simplectization of bi-Hamiltonian structures ⋮ Quasiclassical approximation for models of spin-spin interaction on a one-dimensional lattice ⋮ Asymptotics of the Hartree operator spectrum near the upper boundaries of spectral clusters: asymptotic solutions localized near a circle

Cites Work

• Application of the method of ordered operators to obtain exact solutions
• Limesräume
• The Vlasov dynamics and its fluctuations in the \(1/N\) limit of interacting classical particles
• Weyl and ordered calculus of noncommuting operators
• Calculus of ordered operators on a factor algebra
• Subelliptic estimates and function spaces on nilpotent Lie groups
• A construction of fundamental solution of Schrödinger's equation on the spheres
• Infinite dimensional Lie transformation groups
• Asymptotic behavior of solutions to certain nonlinear Schrödinger-Hartree equations
• New formula for \(ln\;(e^Ae^B)\) in terms of commutators of \(A\) and \(B\)
• Infinite products and T products of exponentials
• The infinite groups of Lie and Cartan. I: The transitive groups
• Uniform convergence structures
• The Weyl functional calculus
• Quantization and unitary representations
• La structure de Poisson sur l'algèbre symétrique d'une algèbre de Lie nilpotente
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Algebras with general commutation relations and their applications. II. Unitary-nonlinear operator equations