Document Type : Original Paper

Author

• M. Amini

Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University,

Abstract

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.

Keywords

• Gabor system
• Nonharmonic Fourier series
• Deficiency
• Entire functions
• Order of growth