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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.

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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
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URLURL TypeDescription DOIArticle
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.
Funding AgencyGrant Number
Junta de AndalucíaFQM-229
Junta de AndalucíaP06-FQM-01735
Junta de AndalucíaP09-FQM-4643
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
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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. (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23968
Deposited By: Ruth Sustaita
Deposited On:10 Jun 2011 19:51
Last Modified:03 Oct 2019 02:51

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