Izvorni znanstveni članak

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

Sažetak

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.

Ključne riječi

Pseudo-differential operator; Fractional Fourier transform; Schwartz space; Sobolev space; Generalized Fredholm integral equation

Hrčak ID:

157713

URI

https://hrcak.srce.hr/157713

Datum izdavanja:

16.5.2016.

Posjeta: 1.542 *