论文标题
薄边界紧凑子集的平均有理近似
Mean Rational Approximation for Compact Subsets with Thin Boundaries
论文作者
论文摘要
1991年，J。Thomson获得了$ p^t（μ）的著名分解定理，$ l^t（μ）$的封闭子空间由分析多项式跨越，当$ 1 \ le te <fe。 $ l^t（μ）$由有理函数跨越了杆子，杆子不合理$μ的支撑，当$ \ mathbb c \ setminus k $的零件的直径在下面限制为$。当$ k $的边界不太疯狂时，我们将上述分解定理扩展为$ r^t（k，μ）$。
In 1991, J. Thomson obtained a celebrated decomposition theorem for $P^t(μ),$ the closed subspace of $L^t(μ)$ spanned by the analytic polynomials, when $1 \le t < ı.$ In 2008, J. Brennan \cite{b08} generalized Thomson's theorem to $R^t(K, μ),$ the closed subspace of $L^t(μ)$ spanned by the rational functions with poles off a compact subset $K$ containing the support of $μ,$ when the diameters of the components of $\mathbb C\setminus K$ are bounded below. We extend the above decomposition theorems for $R^t(K, μ)$ when the boundary of $K$ is not too wild.
