A convolution theorem for the polynomial fourier transform

The polynomial Fourier transform (PFT) is a useful mathematical tool for many areas, including applied mathematics, engineering and signal processing. Some properties and applications for this transform are already known, but an existence of the PFT's convolution theorem is still unknown. The purpose of this paper is to introduce a convolution theorem for the PFT, which has the elegance and simplicity comparable to that of the Fourier Transform (FT). The classical result in the FT domain is shown to be a special case of our achieved theorem.