论文标题
关于磁盘上函数代数的注释
A note on function algebras on disks
论文作者
论文摘要
让$ d $成为以$ d $上$ f，$ f，$ f，$ f，$ f，$ f，$ f，$ f $ d $的封闭磁盘。令$ p [f，g; d] $（res。$ r [f，g; d]）$）是变量$ f $和$ g $的$ d $ polyenmials（res。有理功能）的统一关闭。在\ cite {os}中，使用复杂的动态系统，O'Farrell和Sanabria-garcia证明了$ \ {\ big（z^2，\ cfrac {\ cfrac {\ overline z} {1+\ overline {z}}} \ big） $ p [z^2，\ cfrac {\ overline z} {1+ \ overline z}; d] \ ne c（d）$如果$ d $足够小。在本文中，我们首先给出了两个紧凑型$ \ bbb c^n $的合理凸度的条件，并申请表明$ r [z^2，\ cfrac {\ overline z} {1+ \ overline z}; d] = c（d）$ for $ d $ hill
Let $D$ be a closed disk in the complex plane centered at the origin, $f, g$ complex valued continuous function on $D$. Let $P[f,g; D]$ (res. $R[f, g; D])$) be the uniform closure on $D$ of polynomials (res. rational functions) in variables $f$ and $g$. In \cite{OS}, using complex dynamical systems, O'Farrell and Sanabria-Garcia proved that $\{\Big(z^2, \cfrac{\overline z}{1+\overline{z}}\Big): z\in D\}$ is not polynomially convex with $D$ small enough and so that $P[z^2,\cfrac{\overline z}{1+\overline z}; D]\ne C(D)$ if $D$ is sufficient small. In this paper, we first give a certain conditions for rational convexity of union of two compact set of $\Bbb C^n$ and apply to show that $R[z^2, \cfrac{\overline z}{1+\overline z}; D]= C(D)$ for all $D$ small enough
