Date: Steve Heilman, CIMS
Orthogonal Polynomials with Respect to SelfSimilar Measures
Authors: Steven M. Heilman, Philip Owrutsky, and Robert S. Strichartz
http://arxiv.org/abs/0910.0631
We study experimentally systems of orthogonal polynomials with
respect to selfsimilar 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 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 $x$.
