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arXiv · 2301.06353

Composition operators on Gelfand-Shilov classes

Héctor Ariza·Carmen Fernández·Antonio Galbis
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Abstract

We study composition operators on global classes of ultradifferentiable functions of Beurling type invariant under Fourier transform. In particular, for the classical Gelfand-Shilov classes $\Sigma_d,\ d > 1,$ we prove that a necessary condition for the composition operator $f\mapsto f\circ \psi$ to be well defined is the boundedness of $\psi'.$ We find the optimal index $d'$ for which $C_\psi(\Sigma_d({\mathbb R}))\subset \Sigma_{d'}({\mathbb R})$ holds for any non-constant polynomial $\psi.$

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Héctor Ariza, Carmen Fernández, Antonio Galbis. 2023-01-16. Composition operators on Gelfand-Shilov classes. https://arxiv.org/abs/2301.06353

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