Cyclicity in Dirichlet-type spaces and extremal polynomials

For functions f in Dirichlet-type spaces , we study how to determine constructively optimal polynomials p n that minimize among all polynomials p of degree at most n . We then obtain sharp estimates for the rate of decay of as n approaches ∞, for certain classes of functions f . Finally, inspired by...

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Bibliographic Details
Published in:Journal d'analyse mathématique (Jerusalem) 2015-04, Vol.126 (1), p.259-286
Main Authors: Bénéteau, Catherine, Condori, Alberto A., Liaw, Constanze, Seco, Daniel, Sola, Alan A.
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Analysis
Computation
Construction
Dynamical Systems and Ergodic Theory
Estimates
Functional Analysis
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Optimization
Partial Differential Equations
Polynomials
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Summary:For functions f in Dirichlet-type spaces , we study how to determine constructively optimal polynomials p n that minimize among all polynomials p of degree at most n . We then obtain sharp estimates for the rate of decay of 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.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-015-0017-1