A family of pseudo-differential operators on the Schwartz space associated with the fractional Fourier transform - Srivastava, H. M.; Upadhyay, S. K.; Khatterwani, K. (Russian journal of mathematical physics, 2017)
Motivated essentially by their potential for applications in the mathematical, physical, and engineering sciences, the authors introduce and investigate various useful properties of a family of pseudo-differential operators on the Schwartz space S (ℝ) (i.e., the space of rapidly decreasing infinitely differentiable functions on ℝ), which are associated with the fractional Fourier transform of order α (0 < α ≦ 1). Relevant connections with several related recent developments on this subject are also pointed out.