Nonorthogonal wavelet approximation with rates of deterministic signals
G.A Anastassiou, Stamatis Cambanis · Carolina Digital Repository (University of North Carolina at Chapel Hill) · 2021
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 ϕ fulfills the partition of unity property, and it is of compact support. The asymptotic expansion involves only even terms of products of integrals involving ϕ with integrals of squares of (the first [ only) derivatives of f.