Pyramidal Algorithms for Littlewood-Paley Decompositions

Abstract

It is well known that a pyramidal algorithm is associated with any usual multiresolution analysis of $L^2 (I\mathbb{R})$ for the computation of the corresponding wavelet coefficients. It is shown that an approximate pyramidal algorithm may be associated with more general Littlewood–Paley decompositions. Accuracy estimates are provided for such approximate algorithms. Finally, some explicit examples are studied.