Search results for "Space of rapidly decreasing functions"

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Composition operators on the Schwartz space

2018

[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.

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 APLICADAMathematicsRevista Matemática Iberoamericana
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Dynamics and spectra of composition operators on the Schwartz space

2017

[EN] In this paper we study the dynamics of the composition operators defined in the Schwartz space of rapidly decreasing functions. We prove that such an operator is never supercyclic and, for monotonic symbols, it is power bounded only in trivial cases. For a polynomial symbol ¿ of degree greater than one we show that the operator is mean ergodic if and only if it is power bounded and this is the case when ¿ has even degree and lacks fixed points. We also discuss the spectrum of composition operators.

Space of rapidly decreasing functionsMathematics::Functional AnalysisPure mathematicsComposition operator010102 general mathematicsSpectrum (functional analysis)Power bounded operatorMonotonic functionFixed pointMean ergodic composition operator01 natural sciencesFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsOperator (computer programming)Schwartz spaceBounded functionSpectrumFOS: MathematicsErgodic theory0101 mathematicsMATEMATICA APLICADAAnalysisMathematics
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