The Solvability of a Class of Convolution Equations Associated with 2D FRFT

Zhen-Wei Li, Wen-Biao Gao and Bing-Zhao Li
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Zhen-Wei Li: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, China
Wen-Biao Gao: Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 102488, China
Bing-Zhao Li: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, China

Mathematics, 2020, vol. 8, issue 11, 1-12

Abstract: In this paper, the solvability of a class of convolution equations is discussed by using two-dimensional (2D) fractional Fourier transform (FRFT) in polar coordinates. Firstly, we generalize the 2D FRFT to the polar coordinates setting. The relationship between 2D FRFT and fractional Hankel transform (FRHT) is derived. Secondly, the spatial shift and multiplication theorems for 2D FRFT are proposed by using this relationship. Thirdly, in order to analyze the solvability of the convolution equations, a novel convolution operator for 2D FRFT is proposed, and the corresponding convolution theorem is investigated. Finally, based on the proposed theorems, the solvability of the convolution equations is studied.

Keywords: fractional Fourier transform; convolution theorem; solvability; convolution integral equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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