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Explicit inequalities for wavelet coefficients. (English) Zbl 1018.42022
Summary: A fundamental principle for many applications of wavelets is that the size of the wavelet coefficients indicates the local smoothness of the represented function \(f\). We show how explicit and best possible a priori bounds for wavelet coefficients can be obtained for any wavelet from the coefficients of its two scale relation.
MSC:
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65T60 Numerical methods for wavelets
41A15 Spline approximation
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