RT Journal Article
T1 Cyclicity in Dirichlet-type spaces and extremal polynomials
A1 Bénéteau, Catherine
A1 Condori, Alberto A.
A1 Liaw, Constanze
A1 Seco Forsnacke, Daniel
A1 Sola, Alan A.
AB 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 ∞, for certain classes of functions f. Finally, inspired by the Brown-Shields conjecture, we prove that certain logarithmic conditions on f imply cyclicity, and we study some computational phenomena pertaining to the zeros of optimal polynomials.
PB Springer Nature
SN 0021-7670
YR 2015
FD 2015-04
LK https://hdl.handle.net/10016/32636
UL https://hdl.handle.net/10016/32636
LA eng
NO 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.
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RD 1 sept. 2024