Nonharmonic Gabor Expansions

We consider gabor systems generated by a gaussian function and prove certain classical results of paley and wiener on nonharmonic fourier series of complex exponentials for the gabor expansion‎. ‎in particular, we prove a version of plancherel-po ?lya theorem for entire functions with finite order of growth and use the hadamard factorization theorem to study regularity‎, ‎exactness and deficiency of gabor systems.