Composition operators on the Schwartz space

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 06 Feb 2018Embargo end date: 01 Jan 2015 Spain Publisher:European Mathematical Society - EMS - Publishing House GmbHJournal:Revista Matemática Iberoamericana, volume 34, pages 397-412 (issn: 0213-2230, eissn: 2235-0616,

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Authors: GALBIS VERDU, ANTONIO; Jorda Mora, Enrique;

doi: 10.4171/rmi/989 , 10.48550/arxiv.1511.03072

arXiv: 1511.03072

Composition operators on the Schwartz space

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Abstract

We study composition operators on the Schwartz space of rapidly decreasing functions. We prove that such a composition operator is never a compact operator and we obtain necessary or sufficient conditions for the range of the composition operator to be closed. These conditions are expressed in terms of multipliers for the Schwartz class and the closed range property of the corresponding operator considered in the space of smooth functions.

Country

Spain

Related Organizations

University of Valencia
Spain
Universitat Politècnica de València
Spain

Keywords

Space of rapidly decreasing functions, Mathematics - Functional Analysis, 47B33, 46F05, 47A05, Composite function problem, FOS: Mathematics, Composition operator, MATEMATICA APLICADA, Functional Analysis (math.FA)

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