Analyticity of the generalized two-dimensional fractional cosine transform

Abstract

Fourier transform can be generalized into the fractional Fourier transform (FRFT), Linear Canonical Transform (LCT) and simplified fractional Fourier transform (SFRFT). They extend the utilities of original Fourier transform, and can solve many problems that can't solved well by original Fourier transform.

In this paper, we study distributional generalized two-dimensional fractional Cosine transform. Testing function space  and distributional two-dimensional fractional Cosine transform is defined. Analyticity of the generalized two-dimensional fractional Cosine transform is proved.