Bibliographic Details
| Title: |
The Solvability of a Class of Convolution Equations Associated with 2D FRFT |
| Authors: |
Zhen-Wei Li, Wen-Biao Gao, Bing-Zhao Li |
| Source: |
Mathematics ; Volume 8 ; Issue 11 ; Pages: 1928 |
| Publisher Information: |
Multidisciplinary Digital Publishing Institute |
| Publication Year: |
2020 |
| Collection: |
MDPI Open Access Publishing |
| Subject Terms: |
fractional Fourier transform, convolution theorem, solvability, convolution integral equation |
| Description: |
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. |
| Document Type: |
text |
| File Description: |
application/pdf |
| Language: |
English |
| Relation: |
C1: Difference and Differential Equations; https://dx.doi.org/10.3390/math8111928 |
| DOI: |
10.3390/math8111928 |
| Availability: |
https://doi.org/10.3390/math8111928 |
| Rights: |
https://creativecommons.org/licenses/by/4.0/ |
| Accession Number: |
edsbas.A6DDAE8C |
| Database: |
BASE |
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