  A quantization scheme based on the extension of phase space with application
of constrained quantization technic is considered. The obtained method is
similar to the geometric quantization. For constrained systems the problem of
scalar product on the reduced Hilbert space is investigated and possible
solution of this problem is done. Generalization of the Gupta-Bleuler like
conditions is done by the minimization of quadratic fluctuations of quantum
constraints. The scheme for the construction of generalized coherent states is
considered and relation with Berezin quantization is found. The quantum
distribution functions are introduced and their physical interpretation is
discussed.
