CaltechAUTHORS
  A Caltech Library Service

Asymptotics of the L^2 norm of derivatives of OPUC

Martínez-Finkelshtein, Andrei and Simon, Barry (2011) Asymptotics of the L^2 norm of derivatives of OPUC. Journal of Approximation Theory, 163 (6). pp. 747-778. ISSN 0021-9045. https://resolver.caltech.edu/CaltechAUTHORS:20110610-081439616

[img] PDF - Submitted Version
See Usage Policy.

265Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20110610-081439616

Abstract

We show that for many families of OPUC, one has ‖φ'_n‖2/n → l, a condition we call normal behavior. We prove that this implies |α_n|→0 and that it holds if ∑^∞_(n=0)│α_n│< ∞. We also prove it is true for many sparse sequences. On the other hand, it is often destroyed by the insertion of a mass point.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.jat.2010.09.002 DOIArticle
http://www.sciencedirect.com/science/article/pii/S0021904510001528PublisherArticle
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:© 2010 Elsevier Inc. Received 28 May 2010; received in revised form 23 August 2010; accepted 15 September 2010. Available online 21 September 2010. Communicated by Leonid Golinskii. We dedicate this paper in fond memory of Franz Peherstorfer from whom we learned so much. The first author was supported in part by Junta de Andalucía grants FQM-229, P06-FQM-01735 and P09-FQM-4643, and by the Ministry of Science and Innovation of Spain (project code MTM2008-06689-C02-01). The second author was supported in part by NSF grant DMS-0652919.
Funders:
Funding AgencyGrant Number
Junta de AndalucíaFQM-229
Junta de AndalucíaP06-FQM-01735
Junta de AndalucíaP09-FQM-4643
NSFDMS-0652919
Ministry of Science and Innovation (Spain)MTM2008-06689-C02-01
Subject Keywords:Orthogonal polynomials; Derivative asymptotics
Issue or Number:6
Record Number:CaltechAUTHORS:20110610-081439616
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20110610-081439616
Official Citation:Andrei Martinez-Finkelshtein, Barry Simon, Asymptotics of the L2 norm of derivatives of OPUC, Journal of Approximation Theory, Volume 163, Issue 6, Dedicated to the memory of Franz Peherstorfer, June 2011, Pages 747-778, ISSN 0021-9045, DOI: 10.1016/j.jat.2010.09.002. (http://www.sciencedirect.com/science/article/pii/S0021904510001528)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23968
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:10 Jun 2011 19:51
Last Modified:03 Oct 2019 02:51

Repository Staff Only: item control page