A generalized Fourier transform of the P-quasi distribution function

. In the paper we made a generalization of the Fourier transform in the complex space, applicable to the pair of Husimi’s and P -quasi distributions, in the representation of nonlinear coherent states. Implicitly, our result is a generalization of Mehta's similar result, but which referred only to the canonical coherent states (associated with the one-dimensional harmonic oscillator). Our result is valid for both types of coherent states (defined in the Barut-Girardello, respectively Klauder-Perelomov manner).