2011/10/27 by King, Emily J.
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1110.6061
In order to have a multiresolution analysis, the scaling function must be refinable. That is, it must be the linear combination of 2-dilation, ℤ-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.