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On the growth of the polynomial entropy integrals for measures in the Szegö class
Langue
en
Article de revue
Ce document a été publié dans
Adv. in Maths. 2013, vol. 241, p. 18-32
Résumé en anglais
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 ...Lire la suite >
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).< Réduire
Mots clés en anglais
Entropy integrals
orthogonal polynomials
Schur parameters
Szegö class.
Szegö class
Origine
Importé de halUnités de recherche