6533b82bfe1ef96bd128d80a

RESEARCH PRODUCT

Composition operators on the Schwartz space

Enrique JordáAntonio Galbis

subject

Space of rapidly decreasing functionsPure mathematicsClass (set theory)Composition operatorGeneral MathematicsComposite function problem010102 general mathematicsComposition (combinatorics)Space (mathematics)Compact operator01 natural sciencesFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsRange (mathematics)47B33 46F05 47A05Operator (computer programming)Schwartz spaceFOS: MathematicsComposition operator0101 mathematicsMATEMATICA APLICADAMathematics

description

[EN] 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.

yearjournalcountryeditionlanguage
2018-01-01Revista Matemática Iberoamericana
https://doi.org/10.4171/rmi/989