Pseudo-differential operator associated with the fractional Fourier transform

Akhilesh Prasad, Praveen Kumar
2016 COMMUNICATIONS 115 Math. Commun   unpublished
The main goal of this paper is to study properties of the fractional Fourier transform on Schwartz type space S θ. Symbol class S m,θ ρ,σ is introduced. The fractional pseudo-differential operators (f.p.d.o.) associated with the symbol a(x, ξ) are a continuous linear mapping of S into S θ. Kernel and integral representations of f.p.d.o are obtained. The boundedness property of f.p.d.o. is studied. Application of the fractional Fourier transform in solving a generalized Fredholm integral equation is also given.