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arXiv · 1301.4375

Cyclicity in Dirichlet-type spaces and extremal polynomials

Catherine Bénéteau·Alberto Condori·Constanze Liaw·Daniel Seco·Alan Sola
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Abstract

For functions $f$ in Dirichlet-type spaces we study how to determine constructively optimal polynomials $p_n$ that minimize $\|p f-1\|_α$ among all polynomials $p$ of degree at most $n$. Then we give upper and lower bounds for the rate of decay of $\|p_{n}f-1\|_α$ 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.

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BibTeXRIS

Catherine Bénéteau, Alberto Condori, Constanze Liaw, Daniel Seco, Alan Sola. 2013-01-25. Cyclicity in Dirichlet-type spaces and extremal polynomials. https://doi.org/10.1007/s11854-015-0017-1

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