## 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

### Keywords:

wavelet decompositions
Full Text: