Date:  Steve Heilman, CIMS

Orthogonal Polynomials with Respect to Self-Similar 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 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 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 $x$.