论文标题
将C^k功能从开放集扩展到R，并带有应用
On extending C^k functions from an open set to R, with applications
论文作者
论文摘要
对于$ k \ in \ n \ cup \ {\ infty \} $和$ u $ in $ \ r $中的$ u $打开，让$ \ c^{\，k}（u）$是$ u $上的真实有价值函数，并连续使用第一个$ k $ derivatives。它以$ f \ in \ c^{\，k}（u）$显示为$ g \ in \ ck {\ infty} $，带有$ u \ sbq \ coz g $和$ h \ in \ ck {k ck {k} $，带有$ fg \ res_u = hs_u = h \ res_u $。函数$ f $及其$ k $衍生产品不被认为是$ u $的。函数$ g $是使用基于MolliFier函数的花样构建的。从此推导出关于环$ \ ck {k} $的某些后果，特别是$ \ qcl（\ ck {k}）= \ text {q}（\ ck {k {k}）$。
For $k\in \N\cup \{\infty\}$ and $U$ open in $ \R$, let $\C^{\,k}(U)$ be the ring of real valued functions on $U$ with the first $k$ derivatives continuous. It is shown for $f\in \C^{\,k}(U)$ there is $g\in \ck{\infty}$ with $U\sbq \coz g$ and $h\in \ck{k}$ with $fg\res_U=h\res_U$. The function $f$ and its $k$ derivatives are not assumed to be bounded on $U$. The function $g$ is constructed using splines based on the Mollifier function. Some consequences about the ring $\ck{k}$ are deduced from this, in particular that $\qcl(\ck{k}) = \text{Q}(\ck{k})$.
