Spectra and ergodic properties of multiplication and convolution operators on the space S(R)

In this paper we investigate the spectra and the ergodic properties of the multiplication operators and the convolution operators acting on the Schwartz space S ( R ) of rapidly decreasing functions, i.e., operators of the form M h : S ( R ) → S ( R ) , f ↦ h f , and C T : S ( R ) → S ( R ) , f ↦ T...

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Bibliographic Details
Published in:Revista matemática complutense 2022, Vol.35 (3), p.739-762
Main Authors: Albanese, Angela A., Mele, Claudio
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Convolution
Ergodic processes
Geometry
Mathematics
Mathematics and Statistics
Operators
Spectra
Topology
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Summary:In this paper we investigate the spectra and the ergodic properties of the multiplication operators and the convolution operators acting on the Schwartz space S ( R ) of rapidly decreasing functions, i.e., operators of the form M h : S ( R ) → S ( R ) , f ↦ h f , and C T : S ( R ) → S ( R ) , f ↦ T ⋆ f . Precisely, we determine their spectra and characterize when those operators are power bounded and mean ergodic.
ISSN:1139-1138
1988-2807
DOI:10.1007/s13163-021-00403-0