Abstract
In this paper we give a method to characterize the smoothness of functions inL 1 by anr-regular multiresolution analysis and its derivatives.
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References
J.M. Combes, A. Grossmann and PH. Tchamitchian (Eds.), Wavelets: Time-frequency Methods and Phase Spaces, Springer-Verlag, 1987.
I. Daubechies, Orthonormal Bases of Compactly Supported Wavelets,Commun. Pure Appli. Math.,41 (1988), 909–996.
I. Daubechies, A. Grossmann and Y. Meyer, Painless Non-orthogonal Expansions,J. Math. Phys.,110 (1987), 601–615.
S. Mallat, A Theory for Multiresolution Signal Decomposition: The Wavelet Representation,IEEE Trans. On Pattern Analysis and Machine Intelligence,11 (1989), 674–693.
S. Mallat, Multiresolution Approximation and Wavelet Orthonormal Bases ofL 2,Trans. Amer. Math. Soc.,315 (1989), 69–87.
Y. Meyer, Wavelets and Operators, Hermann, 1990.
Guo Zhurui and Zhou Dingxuan, On Wavelet Analysis and its Derivatives, to appear.
H. Johnen and K. Scherer, On Equivalence ofK-functional and Moduli of Continuity and Some Applications, Lecture Notes in Math., 571, Springer-Verlag, 119–140.
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This project is supported by Zhejiang Provincial Natural Science Foundation and the Special Program of China.
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Zhou, D. On wavelets inL 1 . Acta Mathematicae Applicatae Sinica 10, 69–74 (1994). https://doi.org/10.1007/BF02006260
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DOI: https://doi.org/10.1007/BF02006260