Poisson symmetry algebras and the asymptotics of spectral series
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.
scientific article; zbMATH DE number 4024347
scientific article