6533b834fe1ef96bd129e07c

RESEARCH PRODUCT

Dynamics and spectra of composition operators on the Schwartz space

Antonio GalbisCarmen FernándezEnrique Jordá

subject

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

description

[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.

yearjournalcountryeditionlanguage
2017-07-12
10.13039/501100003359https://dx.doi.org/10.1016/j.jfa.2017.11.005