Published 2012 | Version public
Journal Article

A new approach to ratio asymptotics for orthogonal polynomials

Creators

Abstract

We use a non-linear characterization of orthonormal polynomials due to Saff in order to prove an equivalence of norm asymptotics and strong asymptotics for polynomials. Several applications of this equivalence are also discussed. One of our main results is that for regular measures on the closed unit disk - including, but not limited to the unit circle - or the interval [-2,2], one has ratio asymptotics along a sequence of asymptotic density 1.

Additional Information

© 2012 European Mathematical Society. Received December 10, 2011; revised March 1, 2012. It is a pleasure to thank my advisor Barry Simon for his guidance during this research and Vilmos Totik for useful feedback on an early draft of this work. Many thanks are also due to the anonymous referees for many suggestions about the content and exposition of this paper. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1144469.

Additional details

Identifiers

Eprint ID
35776
DOI
10.4171/JST/34
Resolver ID
CaltechAUTHORS:20121204-081433867

Related works

Describes
10.4171/JST/34 (DOI)

Funding

NSF Graduate Research Fellowship
DGE-1144469

Dates

Created
2012-12-05
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Updated
2021-11-09
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