PSEUDODIFFERENTIAL OPERATORS AND A CANONICAL OPERATOR IN GENERAL SYMPLECTIC MANIFOLDS

Abstract

A calculus of -pseudodifferential operators with symbols on is defined modulo on a closed symplectic manifold under the condition that . The class is described. On Lagrangian submanifolds a class in obstructing the definition of a canonical operator on is found. It is shown that an analogus calculus of pseudodifferential operators can be constructed with respect to homogeneity from an action of the group on . Bibliography: 22 titles.