On the estimation of wavelet coefficients.

In wavelet representations, the magnitude of the wavelet coefficients depends on both the smoothness of the represented function f and on the wavelet. We investigate the extreme values of wavelet coefficients for the standard function spaces Ak=f∥fk)∥2 ≤ 1}, k∈N. In particular, we compare two important families of wavelets in this respect, the orthonormal Daubechies wavelets and the semiorthogonal spline wavelets. Deriving the precise asymptotic values in both cases, we show that the spline constants are considerably smalle