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Perturbation of Wavelet Frames of Quaternionic-Valued Functions

Author

Listed:
  • Fusheng Xiao

    (School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China)

  • Jianxun He

    (School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China)

Abstract

Let L 2 ( R , H ) denote the space of all square integrable quaternionic-valued functions. In this article, let Φ ∈ L 2 ( R , H ) . We consider the perturbation problems of wavelet frame { Φ m , n , a 0 , b 0 , m , n ∈ Z } about translation parameter b 0 and dilation parameter a 0 . In particular, we also research the stability of irregular wavelet frame { S m Φ ( S m x − n b ) , m , n ∈ Z } for perturbation problems of sampling.

Suggested Citation

  • Fusheng Xiao & Jianxun He, 2021. "Perturbation of Wavelet Frames of Quaternionic-Valued Functions," Mathematics, MDPI, vol. 9(15), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1807-:d:605044
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