Nonorthogonal wavelet approximation with rates of deterministic signals

An n(th) order asymptotic expansion is produced for the L-2-error in a nono rthogonal tin general) wavelet approximation at resolution 2(-k) of determi nistic signals f. These signals over the whole real line are assumed to hav e n continuous derivatives of bounded variation. The engaged nonorthogonal tin general) scale function phi fulfills the partition of unity property, a nd it is of compact support. The asymptotic expansion involves only even te rms of products of integrals involving phi with integrals of squares of (th e first [n/2] - 1 only) derivatives of f. (C) 2000 Elsevier Science Ltd; Al i rights reserved.