论文标题
加权$ \ ell^p_a $的多项式循环方法
Polynomial approach to cyclicity for weighted $\ell^p_A$
论文作者
论文摘要
在以前的作品中，基于对所谓的\ emph {最佳多项式近似值}的研究，已经提出了一种循环功能研究中循环功能的方法。在本文中，我们将这种方法扩展到了（非希尔伯特）分析功能的案例，其泰勒系数为$ \ ell^p（ω）$，对于某些权重$ω$。当$ω= \ {（k+1）^α\} _ {k \ in \ mathbb {n}} $，对于固定的$α\ in \ mathbb {r} $而言，我们得出了$ 1 <p <p <p <\ innd narm nard conferge cornegeng conferge conferge conferge的表征。
In previous works, an approach to the study of cyclic functions in reproducing kernel Hilbert spaces has been presented, based on the study of so called \emph{optimal polynomial approximants}. In the present article, we extend such approach to the (non-Hilbert) case of spaces of analytic functions whose Taylor coefficients are in $\ell^p(ω)$, for some weight $ω$. When $ω=\{(k+1)^α\}_{k\in \mathbb{N}}$, for a fixed $α\in \mathbb{R}$, we derive a characterization of the cyclicity of polynomial functions and, when $1<p<\infty$, we obtain sharp rates of convergence of the optimal norms.
