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

Author

Listed:
  • 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
    Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 102488, China)

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.

Suggested Citation

  • Zhen-Wei Li & Wen-Biao Gao & Bing-Zhao Li, 2020. "The Solvability of a Class of Convolution Equations Associated with 2D FRFT," Mathematics, MDPI, vol. 8(11), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1928-:d:438798
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    References listed on IDEAS

    as
    1. Yong-Gang Li & Bing-Zhao Li & Hua-Fei Sun, 2014. "Uncertainty Principles for Wigner-Ville Distribution Associated with the Linear Canonical Transforms," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, May.
    2. Luc Robbiano & Qiong Zhang, 2020. "Logarithmic Decay of Wave Equation with Kelvin-Voigt Damping," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    3. Li, Pingrun, 2019. "Singular integral equations of convolution type with Cauchy kernel in the class of exponentially increasing functions," Applied Mathematics and Computation, Elsevier, vol. 344, pages 116-127.
    4. Hongzhou Wang, 2020. "Boundary Value Problems for a Class of First-Order Fuzzy Delay Differential Equations," Mathematics, MDPI, vol. 8(5), pages 1-9, May.
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    Cited by:

    1. Siddiqui Saima & Bingzhao Li & Samad Muhammad Adnan, 2022. "New Sampling Expansion Related to Derivatives in Quaternion Fourier Transform Domain," Mathematics, MDPI, vol. 10(8), pages 1-12, April.

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