Cyclicity in Dirichlet-type spaces and extremal polynomials

Bénéteau, Catherine; Condori, Alberto A.; Liaw, Constanze; Seco Forsnacke, Daniel; Sola, Alan A.

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Cyclicity in Dirichlet-type spaces and extremal polynomials

Author(s): Bénéteau, Catherine; Condori, Alberto A.; Liaw, Constanze; Seco Forsnacke, Daniel; Sola, Alan A.

Publisher: Springer Nature

Issued date: 2015-04

Citation: Bénéteau, C., Condori, A. A., Liaw, C., Seco, D. & Sola, A. A. (2015). Cyclicity in Dirichlet-type spaces and extremal polynomials. Journal d’Analyse Mathématique, 126(1), pp. 259–286.

ISSN: 0021-7670

DOI: https://doi.org/10.1007/s11854-015-0017-1

xmlui.dri2xhtml.METS-1.0.item-contributor-funder: Ministerio de Ciencia e Innovación (España)

Sponsor: CB, DS, and AS would like to thank the Institut Mittag-Leffler and the AXA Research Fund for support while working on this project. CL is partially supported by the NSF grant DMS-1261687. DS is supported by the MEC/MICINN grant MTM-2008-00145. AS acknowledges support from the EPSRC under grant EP/103372X/1.

Project: Gobierno de España. MTM2008-00145

Keywords: Bergman space , Optimal norm , Open unit disk , Dirichlet space , Closed disk

URI: http://hdl.handle.net/10016/32636

Abstract:

For functions f in Dirichlet-type spaces Dα, we study how to determine constructively optimal polynomials p n that minimize ∥pf−1∥α among all polynomials p of degree at most n. We then obtain sharp estimates for the rate of decay of ∥pnf−1∥α as n approaches ∞, [+]

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