A Matricial Algorithm for Polynomial Refinement
Information Theory
2011-11-02 v2 math.IT
Abstract
In order to have a multiresolution analysis, the scaling function must be refinable. That is, it must be the linear combination of 2-dilation, -translates of itself. Refinable functions used in connection with wavelets are typically compactly supported. In 2002, David Larson posed the question in his REU site, "Are all polynomials (of a single variable) finitely refinable?" That summer the author proved that the answer indeed was true using basic linear algebra. The result was presented in a number of talks but had not been typed up until now. The purpose of this short note is to record that particular proof.
Cite
@article{arxiv.1110.6061,
title = {A Matricial Algorithm for Polynomial Refinement},
author = {Emily J. King},
journal= {arXiv preprint arXiv:1110.6061},
year = {2011}
}