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2011 Orthogonal Polynomials with Respect to Self-Similar Measures
Steven M. Heilman, Philip Owrutsky, Robert S. Strichartz
Experiment. Math. 20(3): 238-259 (2011).

Abstract

We study experimentally systems of orthogonal polynomialswith respect to self-similar measures. When the support of the measure is a Cantor set, we observe some interesting properties of the polynomials, both on the Cantor set and in the gaps of the Cantor set. We introduce an effective method to visualize the graph of a function on a Cantor set. We suggest a new perspective, based on the theory of dynamical systems, for studying families $P_n(x)$ of orthogonal functions as functions of $n$ for fixed values of $x$.

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Steven M. Heilman. Philip Owrutsky. Robert S. Strichartz. "Orthogonal Polynomials with Respect to Self-Similar Measures." Experiment. Math. 20 (3) 238 - 259, 2011.

Information

Published: 2011
First available in Project Euclid: 6 October 2011

zbMATH: 1262.33010
MathSciNet: MR2836250

Subjects:
Primary: 33C45
Secondary: 28A80

Keywords: dynamical systems , orthogonal polynomials , self-similar measures

Rights: Copyright © 2011 A K Peters, Ltd.

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Vol.20 • No. 3 • 2011
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