Published June 2011
| Version Submitted
Journal Article
Open
Asymptotics of the L^2 norm of derivatives of OPUC
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1.
University of Almería
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2.
California Institute of Technology
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.Attached Files
Submitted - p330.pdf
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p330.pdf
Additional details
Identifiers
- Eprint ID
- 23968
- DOI
- 10.1016/j.jat.2010.09.002
- Resolver ID
- CaltechAUTHORS:20110610-081439616
Related works
- Describes
- 10.1016/j.jat.2010.09.002 (DOI)
Funding
- Junta de Andalucía
- FQM-229
- Junta de Andalucía
- P06-FQM-01735
- Junta de Andalucía
- P09-FQM-4643
- NSF
- DMS-0652919
- Ministry of Science and Innovation (Spain)
- MTM2008-06689-C02-01
Dates
- Created
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2011-06-10Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field
Caltech Custom Metadata
- Caltech groups
- Mathematics Department , Physics Department