Perturbation of Wavelet Frames of Quaternionic-Valued Functions

Fusheng Xiao and Jianxun He
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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

Mathematics, 2021, vol. 9, issue 15, 1-12

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.

Keywords: wavelet frame; quaternionic-valued function; perturbation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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