Perturbation of Wavelet Frames of Quaternionic-Valued Functions

Let L2(R,H) denote the space of all square integrable quaternionic-valued functions. In this article, let Φ∈L2(R,H). We consider the perturbation problems of wavelet frame {Φm,n,a0,b0,m,n∈Z} about translation parameter b0 and dilation parameter a0. In particular, we also research the stability of ir...

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Bibliographic Details
Published in:Mathematics (Basel) 2021-08, Vol.9 (15), p.1807
Main Authors: Xiao, Fusheng, He, Jianxun
Format: Article
Language:English
Subjects:
Fourier transforms
Mathematical functions
Mathematics
Parameters
Perturbation
quaternionic-valued function
Signal processing
Theorems
wavelet frame
Wavelet transforms
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Summary:Let L2(R,H) denote the space of all square integrable quaternionic-valued functions. In this article, let Φ∈L2(R,H). We consider the perturbation problems of wavelet frame {Φm,n,a0,b0,m,n∈Z} about translation parameter b0 and dilation parameter a0. In particular, we also research the stability of irregular wavelet frame {SmΦ(Smx−nb),m,n∈Z} for perturbation problems of sampling.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9151807