Abstract
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 map** 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.
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Translated from Matematicheskie Zametki, 2023, Vol. 114, pp. 297–305 https://doi.org/10.4213/mzm13690.
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Rakhimova, A.I. On Hypercyclic Operators in Weighted Spaces of Infinitely Differentiable Functions. Math Notes 114, 242–249 (2023). https://doi.org/10.1134/S0001434623070258
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DOI: https://doi.org/10.1134/S0001434623070258