Compactly supported, orthogonal, continuous piecewise polynomial multiresolution analysis
Classical Analysis and ODEs
2026-05-12 v2 Numerical Analysis
Numerical Analysis
Abstract
We present explicit representations in terms of hypergeometric functions for the scaling functions in the orthogonal multiresolution analyses associated with piecewise continuous polynomials. Closed formulas for the Mellin transform of these functions as well as their Fourier transforms are derived. Some new multiresolution analyses whose scaling functions have coefficients that are rational numbers are introduced and discussed.
Cite
@article{arxiv.2412.02908,
title = {Compactly supported, orthogonal, continuous piecewise polynomial multiresolution analysis},
author = {Lidia Fernández and Jeffrey S. Geronimo and Plamen Iliev},
journal= {arXiv preprint arXiv:2412.02908},
year = {2026}
}