Abstract
Frame plays an important role in the theory of wavelet analysis. Frame theory and stability of frames are important topics of wavelet analysis. Recently, people pay more attention to multi-wavelet frames. Among literatures, Chui [2], for instance, give a complete characterization of multi-wavelet frames for arbitrary dilation factor a > 1. There, however, is relatively less results on the stability of multi-wavelet frames. This paper devotes to the study of stability of multi-wavelet frames based on functional analysis methods. The following meaningful results are obtained: firstly, multi-wavelet frames are stable by some kinds of linear operators action; Secondly, multi-wavelet frames are stable over some kinds of perturbations conditions on ψ.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R. Balan, Stability Theorems for fourier frames and wavelet Riesz bases, to appear in Journal of Fourier Analysis and applications.
C. K. Chui, Orthonormal wavelets and Tight Frames with arbitrary real dilations, Applied and Computational Harmonic Analysis, 9(2000), 243–264.
P.G. Casazza, N.J. Katon, Generalizing the Paley-Wiener perturbation theory for Banach space, Proc. Amer. Math. Soc, 127(2)(1999), 519–527.
I. Daubechies, Ten Lectures On Wavelets, CBMS-NSF Regional Conference in Applied Mathematics, SIAM Publ, Philadelphia, (1992), 56–106.
S. Favier, R. Zalik, On the stability of frames and Riesz bases, Applied and Computational Harmonic Analysis, 2(2)(1995), 160–173.
Y. N. Guo, J. Y. Zhou, On the stability and perturbation of Riesz Frames, Acta Mathematica Sinica, 46(4)(2003), 673–682.
Y.C. Zhu, On the stability of q-Frames and p-Riesz bases in Banach space, Chinese Annals of Mathematics, 22A(3)(2001), 359–364.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Birkhäuser Verlag Basel/Switzerland
About this paper
Cite this paper
Wang, G., Cheng, Z. (2006). On the Stability of Multi-wavelet Frames. In: Qian, T., Vai, M.I., Xu, Y. (eds) Wavelet Analysis and Applications. Applied and Numerical Harmonic Analysis. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7778-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-7643-7778-6_9
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7777-9
Online ISBN: 978-3-7643-7778-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)