# Mathematical Communications,Vol. 21 No. 1, 2016

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 EditionPrasad, 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 EditionPrasad, 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 EditionPrasad, 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 HarvardPrasad, 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) VancouverPrasad 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 IEEEA. 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.

Hrčak ID: 157713

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