Pseudo-Differential Operators Involving Fractional Fourier Cosine (Sine) Transform

Akhilesh Prasad, Manoj Kumar Singh

A brief introduction to the fractional Fourier cosine transform as well as fractional Fourier sine transform and their basic properties are given. Fractional Fourier cosine (fractional Fourier sine) transform of tempered distributions is studied. Pseudo-differential operators involving these transformations are investigated and discussed the continuity on certain spaces $\mathcal S_e$ and $\mathcal S_o$.