Uniformization method in the theory of Nonlinear Hamiltonian systems of Vlasov and Hartree type

Possibilities of obtaining the approximate solutions to the equations of the Hartree type from the known solutions of the uniformized linear equations are investigated. Nonlinear hamiltonian systems described by abstract equations of the Vlassov and Hartree type are considered by means of algebraic methods. New notion of the “unif ormization” is introduced which represents the generalization of the second quantization method for arbitrary Hamiltonian (Lie–Jordan) algebras, in particular, for operator algebras in indefinite spaces. Functional calculus of uniformized observables is developed, extending and unifying the calculus of generating functionals of commuting; and anticommuting variables for even operators.