Path integration and operator ordering

Method of constructing the Feynmann path integral for particle in the curved space with the geometry determined by the kinetic energy is suggested. The method is not based on the finite-tuple approximations. It is shown by the example of the system with the Hamiltonian Hsub(cl)=fsup(2)(x)psup(2) (and some others) that the Feynman integral could be obtained from the Gaussian functional by means of substitution of integration variables. This enables to put some operator into correspondence with the function H in the unique way. Procedure of constructing an operator which corresponds to the classical coordinates and momenta function for the given type of Hamiltonian is also considered