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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

Fulltext: english, pdf (164 KB) pages 115-126 downloads: 370* cite
APA 6th Edition
Prasad, A. & Kumar, P. (2016). Pseudo-differential operator associated with the fractional Fourier transform. Mathematical Communications, 21 (1), 115-126. Retrieved from https://hrcak.srce.hr/157713
MLA 8th Edition
Prasad, Akhilesh and Praveen Kumar. "Pseudo-differential operator associated with the fractional Fourier transform." Mathematical Communications, vol. 21, no. 1, 2016, pp. 115-126. https://hrcak.srce.hr/157713. Accessed 24 Jun. 2021.
Chicago 17th Edition
Prasad, Akhilesh and Praveen Kumar. "Pseudo-differential operator associated with the fractional Fourier transform." Mathematical Communications 21, no. 1 (2016): 115-126. https://hrcak.srce.hr/157713
Harvard
Prasad, A., and Kumar, P. (2016). 'Pseudo-differential operator associated with the fractional Fourier transform', Mathematical Communications, 21(1), pp. 115-126. Available at: https://hrcak.srce.hr/157713 (Accessed 24 June 2021)
Vancouver
Prasad A, Kumar P. Pseudo-differential operator associated with the fractional Fourier transform. Mathematical Communications [Internet]. 2016 [cited 2021 June 24];21(1):115-126. Available from: https://hrcak.srce.hr/157713
IEEE
A. Prasad and P. Kumar, "Pseudo-differential operator associated with the fractional Fourier transform", Mathematical Communications, vol.21, no. 1, pp. 115-126, 2016. [Online]. Available: https://hrcak.srce.hr/157713. [Accessed: 24 June 2021]

Abstracts
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
https://hrcak.srce.hr/157713

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