Composition operators on Gelfand-Shilov classes

2023/01/16 by Héctor Ariza, Ariza, Héctor, Carmen Fernández +3 · 2 citations
Mathematics · #46F05 #47B33 #Algebraic and Geometric Analysis #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2301.06353

openalex publication_date 2023/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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 Σ_d, d > 1, we prove that a necessary condition for the composition operator f↦ f∘ ψ to be well defined is the boundedness of ψ'. We find the optimal index d' for which C_ψ(Σ_d(\mathbb R))⊂ Σ_d'(\mathbb R) holds for any non-constant polynomial ψ.

Cited by

• Composition operators on weighted modulation spaces
• Generalized upper and lower Legendre conjugates for Braun-Meise-Taylor weight functions

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• Topologizability and related properties of the iterates of composition operators in Gelfand-Shilov classes
• Iterates of composition operators on global spaces of ultradifferentiable functions
• Decompositions of Gelfand-Shilov kernels into kernels of similar class
• Pseudo-differential operators in a Gelfand-Shilov setting
• Gelfand-Shilov spaces for extended Gevrey regularity