A family of pseudo-differential operators on the Schwartz space associated with the fractional Fourier transform

Abstract

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. © 2017, Pleiades Publishing, Ltd.