Nonorthogonal wavelet approximation with rates of deterministic signals

An nth order asymptotic expansion is produced for the L2-error in a nonorthogonal (in general) wavelet approximation at resolution 2−k of deterministic signals f. These signals over the whole real line are assumed to have n continuous derivatives of bounded variation. The engaged nonorthogonal (in general) scale function fulfills the partition of unity property, and it is of compact support. The asymptotic expansion involves only even terms of products of integrals involving with integrals of squares of (the first [n/2] − 1 only) derivatives of f.