We obtain estimates for Christoffel functions and orthogonal polynomials for even weights W : R → [0, ∞) that are 'close' to indeterminate weights. Our main example is exp fenced(- || fenced(x) fenced(log || fenced(x))β), with β real, possibly modified near 0, but our results also apply to exp fenced(- || fenced(x)α fenced(log || fenced(x))β), α < 1. These types of weights exhibit interesting properties largely because they are either indeterminate or are close to the border between determinacy and indeterminacy in the classical moment problem.
Bibliographical noteFunding Information:
Research supported by NSF Grant DMS 0400446 and US-Israel BSF Grant 2004353. ∗ Corresponding author. Fax: +1 404 894 4409. E-mail addresses: firstname.lastname@example.org (E. Levin), email@example.com (D.S. Lubinsky).