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Composition operators on Gelfand-Shilov classes
- Publication Year :
- 2023
-
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 $\psi.$
- Subjects :
- Mathematics - Functional Analysis
47B33, 46F05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2301.06353
- Document Type :
- Working Paper