Mathematics > Classical Analysis and ODEs
[Submitted on 18 Jan 2013 (v1), last revised 25 Jan 2013 (this version, v2)]
Title:Cyclicity in Dirichlet-type spaces and extremal polynomials
View PDFAbstract:For functions $f$ in Dirichlet-type spaces we study how to determine constructively optimal polynomials $p_n$ that minimize $\|p f-1\|_\alpha$ among all polynomials $p$ of degree at most $n$. Then we give upper and lower bounds for the rate of decay of $\|p_{n}f-1\|_{\alpha}$ as $n$ approaches $\infty$. Further, we study a generalization of a weak version of the Brown-Shields conjecture and some computational phenomena about the zeros of optimal polynomials.
Submission history
From: Daniel Seco [view email][v1] Fri, 18 Jan 2013 13:20:05 UTC (90 KB)
[v2] Fri, 25 Jan 2013 18:45:09 UTC (238 KB)
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