Geodesic
On Hypercyclic Operators in Weighted Spaces of Infinitely Differentiable Functions
Matematičeskie zametki, Tome 114 (2023) no. 2, pp. 297-305

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A differentiation-invariant weighted Fréchet space ${\mathcal E}(\varphi)$ of infinitely differentiable functions in ${\mathbb R}^n$ generated by a countable family $\varphi$ of continuous real-valued functions in ${\mathbb R}^n$ is considered. It is shown that, under minimal restrictions on $\varphi$, any continuous linear operator on ${\mathcal E}(\varphi)$ that is not a scalar multiple of the identity mapping and commutes with the partial differentiation operators is hypercyclic. Examples of hypercyclic operators in ${\mathcal E}(\varphi)$ are presented for cases in which the space ${\mathcal E}(\varphi)$ is translation invariant.
Keywords: infinitely differentiable functions, hypercyclic operator, convolution operator. 
@article{MZM_2023_114_2_a10,
     author = {A. I. Rakhimova},
     title = {On {Hypercyclic} {Operators} in {Weighted} {Spaces} of {Infinitely} {Differentiable} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {297--305},
     publisher = {mathdoc},
     volume = {114},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_2_a10/}
}
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A. I. Rakhimova. On Hypercyclic Operators in Weighted Spaces of Infinitely Differentiable Functions. Matematičeskie zametki, Tome 114 (2023) no. 2, pp. 297-305. http://geodesic.mathdoc.fr/item/MZM_2023_114_2_a10/