zbMATH — the first resource for mathematics

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.
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65T60 Numerical methods for wavelets
41A15 Spline approximation
Full Text: DOI
[1] DOI: 10.1137/0729097 · Zbl 0766.65007 · doi:10.1137/0729097
[2] Chui C.K., Wavelet analysis and its applications 1 (1992)
[3] DOI: 10.2307/2153941 · Zbl 0759.41008 · doi:10.2307/2153941
[4] DOI: 10.1137/0730024 · Zbl 0773.65006 · doi:10.1137/0730024
[5] Daubechies I., CBMS-NSF Regional Conference Series in applied Mathematics 61 (1992)
[6] DOI: 10.1023/A:1019103617219 · Zbl 0902.65097 · doi:10.1023/A:1019103617219
[7] DOI: 10.1023/A:1018998009387 · Zbl 0955.42023 · doi:10.1023/A:1018998009387
[8] Strang, G. and Nguyen, T. 1996. ”Wavelets and Filter Banks”. Wellesley-Cambridge Press. · Zbl 1254.94002
[9] DOI: 10.1016/0165-1684(93)90144-Y · Zbl 0768.41012 · doi:10.1016/0165-1684(93)90144-Y
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.