Poisson symmetry algebras and the asymptotics of spectral series
type: Item
instance of: scholarly article
title: Poisson symmetry algebras and the asymptotics of spectral series
zbMATH Open document ID: 0629.58017
DOI: 10.1007/BF01077310
publication date: 1986-01-01T00:00:00Z
review text: Recalling the connection between the reduction procedure for Hamiltonian systems and Poisson algebras the author introduces the Lagrangian manifold which serves as the oscillation front of the intertwining homomorphism between the reduced and the original phase space. He then defines the oscillation front of the operator of generalized translation which gives the structure of group algebra for nonlinear Poisson brackets. The resulting theorem on the asymptotics of spectral series is formulated and its application to the three-dimensional Schrödinger operator with perturbed central potential is considered.
Mathematics Subject Classification ID: 58J40
Mathematics Subject Classification ID: 35S99
zbMATH DE Number: 4024347
zbMATH Keywords: pseudodifferential operator
zbMATH Keywords: nonlinear Poisson brackets
zbMATH Keywords: three- dimensional Schrödinger operator
author: M. V. Karasev
reviewed by: S. K. Chatterjea
MaRDI profile type: Publication
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4024347