Orthogonal Polynomials with Respect to Self-Similar Measures

Details Orthogonal Polynomials with Respect to Self-Similar Measures Orthogonal Polynomials with Respect to Self-Similar Measures

2009-10-04

arxiv.org/abs/0910.0631v1

Mathematics

Classical Analysis and ODEs

30 pages, 39 figures, 1 table, submitted, Exp. Math

Scientific paper

We study experimentally systems of orthogonal polynomials with 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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