The Solvability of a Class of Convolution Equations Associated with 2D FRFT
| Autor: | Bing-Zhao Li, Zhen-Wei Li, Wen-Biao Gao |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Class (set theory)
Hankel transform lcsh:Mathematics General Mathematics 010102 general mathematics Order (ring theory) 010103 numerical & computational mathematics lcsh:QA1-939 fractional Fourier transform 01 natural sciences Fractional Fourier transform Convolution convolution integral equation Computer Science (miscellaneous) Applied mathematics Multiplication 0101 mathematics Polar coordinate system Convolution theorem Engineering (miscellaneous) solvability convolution theorem Mathematics |
| Zdroj: | Mathematics Volume 8 Issue 11 Mathematics, Vol 8, Iss 1928, p 1928 (2020) |
| ISSN: | 2227-7390 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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