Nonorthogonal wavelet approximation with rates of deterministic signals (Q1570058)

The authors produce an \(n\)th-order asymptotic expansion for the \({\mathcal L}_2\)-error in a nonorthogonal (in general) wavelet approximation at resolution \(2^{-k}\) of deterministic signals \(f\) which have over the whole real line, \(n\) continuous derivatives of bounded variation. The engaged nonorthgonal (in general) scale function \(\varphi\) fulfills the partition of unity property, and it is of compact support. The asymptotic expansion involves only even terms of products of integrals involving \(\varphi\) with integrals of squares of (the first \([n/2]-1\) only) derivatives of \(f\).