论文标题
平滑功能的加权空间之间的组成算子的注释
A note on composition operators between weighted spaces of smooth functions
论文作者
论文摘要
对于某些加权的本地凸空间$ x $和$ y $的一个真实可变光滑函数，我们表征平滑功能$φ：\ mathbb {r} \ to \ mathbb {r} $，为构图操作员$c_φ$c_φ：x \ to y，x \ to y，f \ f \ m mapsto f \ m mapsto f \ f \ f \ f \ compincouncy compont and CONTERCOUND and CONTY and CONTY and CONTY and CONTY and CONTY and CONTY and CONTEN。最近考虑了$ x = y $的问题，是迅速降低光滑功能的空间$ \ mathscr {s} $ [1]和SPACE $ \ MATHSCR {O} _M $缓慢增加平滑功能[2]。特别是，我们恢复了这两个结果，并获得了$ x = y $的特征，即$ \ mathscr {o} _c $非常缓慢地增加平滑功能。
For certain weighted locally convex spaces $X$ and $Y$ of one real variable smooth functions, we characterize the smooth functions $φ: \mathbb{R} \to \mathbb{R}$ for which the composition operator $C_φ: X \to Y, \, f \mapsto f \circ φ$ is well-defined and continuous. This problem has been recently considered for $X = Y$ being the space $\mathscr{S}$ of rapidly decreasing smooth functions [1] and the space $\mathscr{O}_M$ of slowly increasing smooth functions [2]. In particular, we recover both these results as well as obtain a characterization for $X =Y$ being the space $\mathscr{O}_C$ of very slowly increasing smooth functions.
