Original scientific paper
Pseudo-differential operator associated with the fractional Fourier transform
Akhilesh Prasad
; Department of Applied Mathematics, Indian School of Mines, Dhanbad, India
Praveen Kumar
; Department of Applied Mathematics, Indian School of Mines, Dhanbad, India
Abstract
The main goal of this paper is to study properties of the fractional Fourier transform on Schwartz type space $\mathscr{S}_{\theta}$. Symbol class $S_{\rho,\sigma}^{m,\theta}$ is introduced. The fractional pseudo-differential operators (f.p.d.o.) associated with the symbol $a(x,\xi)$ is a continuous linear mapping of $\mathscr{S}_{\theta}$ into itself. Kernel and integral representations of f.p.d.o are obtained. Boundedness property of f.p.d.o. is studied. Application of the fractional Fourier transform in solving generalized Fredholm integral equation is also given.
Keywords
Pseudo-differential operator; Fractional Fourier transform; Schwartz space; Sobolev space; Generalized Fredholm integral equation
Hrčak ID:
157713
URI
Publication date:
16.5.2016.
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