Abstract

Integral transform, fractional integral transform is a flourishing filed of active research due to its wide range of application. Fourier transform, fractional Fourier transform is probably the most intensively studied among all fractional transforms, similarly 2D canonical sine-sine transforms, and 2D canonical cosine-cosine is a powerful mathematical tool for processing images. In this paper the canonical 2D sine-sine transform is define in generalized sense. And various testing functions spaces defined by using Gelfand-shilov technique. Also uniqueness theorem, modulation theorems are proved.