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Article
Balanced Biorthogonal Scaling Vectors Using Fractal Function Macroelements on [0,1]
Applied and Computational Harmonic Analysis
  • Bruce Kessler, Western Kentucky University
Publication Date
11-11-2006
Comments

Copyright 2007, Elsevier Inc. All rights reserved. Posted as the author's final version. Published in Applied and Computational Harmonic Analysis 22 (2007): 286-303.

Abstract

Geronimo, Hardin, et al have previously constructed orthogonal and biorthogonal scaling vectors by extending a spline scaling vector with functions supported on $[0,1]$. Many of these constructions occurred before the concept of balanced scaling vectors was introduced. This paper will show that adding functions on $[0,1]$ is insufficient for extending spline scaling vectors to scaling vectors that are both orthogonal and balanced. We are able, however, to use this technique to extend spline scaling vectors to balanced, biorthogonal scaling vectors, and we provide two large classes of this type of scaling vector, with approximation order two and three, respectively, with two specific constructions with desirable properties in each case. The constructions will use macroelements supported on $[0,1]$, some of which will be fractal functions.

Citation Information
Bruce Kessler. "Balanced Biorthogonal Scaling Vectors Using Fractal Function Macroelements on [0,1]" Applied and Computational Harmonic Analysis Vol. 22 (2006) p. 286 - 303
Available at: http://works.bepress.com/bruce_kessler/6/