Asymptotics of the L^2 norm of derivatives of OPUC

Creators: Martínez-Finkelshtein, Andrei; Simon, Barry

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.

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.

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