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Compression of wavelet decompositions. (English) Zbl 0764.41024

Summary: We characterize functions with a given degree of nonlinear approximation by linear combinations with \(n\) terms of a function \(\varphi\), its dilates and their translates. This gives a unified viewpoint of recent results on nonlinear approximation by spline functions and give their extension to functions of several variables. Our approach is formulated in terms of wavelet decompositions.

MSC:

41A45 Approximation by arbitrary linear expressions
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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