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Poisson symmetry algebras and the asymptotics of spectral series. (English. Russian original) Zbl 0629.58017
Funct. Anal. Appl. 20, 17-26 (1986); translation from Funkts. Anal. Prilozh. 20, No. 1, 21-32 (1986).
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.
Reviewer: S.K.Chatterjea

MSC:
58J40 Pseudodifferential and Fourier integral operators on manifolds
35S99 Pseudodifferential operators and other generalizations of partial differential operators
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