We prove that every hypercyclic weighted composition operator acting on the space of smooth functions on the real line is already frequently hypercyclic. Moreover, for a given frequently hypercyclic weighted composition operator \(C_{w,\psi }\) we show that \(C^\infty ({\mathbb {R}})=FHC(C_{w,\psi })+FHC(C_{w,\psi })\) and that \(FHC(C_{w,\psi })\cup \{0\}\) contains a closed infinite dimensional subspace.

中文翻译：

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加权函数算子在光滑函数空间上的频繁超循环性

我们证明，作用在实线上平滑函数空间上的每个超循环加权合成算子已经是频繁的超循环了。此外，对于给定的频繁超循环加权合成算子\（C_ {w，\ psi} \），我们证明\（C ^ \ infty（{\ mathbb {R}}）= FHC（C_ {w，\ psi}） + FHC（C_ {w，\ psi}）\）和那个\（FHC（C_ {w，\ psi}）\ cup \ {0 \} \）包含一个封闭的无限维子空间。