A note on the limiting procedures for path integrals

Limiting procedures for the Feynman type path integral are considered. The evolution operator is approximated with operators corresponding to the exponential of the Hamiltonian's symbol. The proof of convergence uses Chernoff's theory and its extension on the class of stable operators. The approach is especially adequate for the generalized coherent states path integral, where decomposition of a Hamiltonian into the sums used in the approach based on Trotter's formula may be unnatural