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.
|Number of pages||40|
|Journal||Journal of Approximation Theory|
|State||Published - Aug 2007|
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).