Product and Convolution Theorems for the Fractional Fourier Transform

The fractional Fourier transform (FRFT) is a generalization of the classical Fourier transform (FT). It has recently found applications in several areas, including signal processing and optics. Many properties of this transform are already known, but an extension of the FT?s convolution theorem is still missing. The purpose of this paper is to introduce extensions of this theorem, dealing with the FRFT of a product and of a convolution of two functions.