On the growth of the polynomial entropy integrals for measures in the Szegö class
Language
en
Article de revue
This item was published in
Adv. in Maths. 2013, vol. 241, p. 18-32
English Abstract
Let be a probability Borel measure on the unit circle T and f ng be the orthonormal polynomials with respect to . We say tRhat is a Szego measure, if it has an arbitrary singular part s, and T log 0dm > -∞, 1, where 0 is ...Read more >
Let be a probability Borel measure on the unit circle T and f ng be the orthonormal polynomials with respect to . We say tRhat is a Szego measure, if it has an arbitrary singular part s, and T log 0dm > -∞, 1, where 0 is the density of the absolutely continuous part of , m being the normalized Lebesgue measure on T. The entropy integrals for n are de ned as n = Z T j nj2 log j njd It is not di cult to show that n = o( p n). In this paper, we construct a measure from the Szego class for which this estimate is sharp (over a subsequence of n's).Read less <
English Keywords
Entropy integrals
orthogonal polynomials
Schur parameters
Szegö class.
Szegö class
Origin
Hal imported