2021
DOI: 10.1007/s13163-021-00403-0
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Spectra and ergodic properties of multiplication and convolution operators on the space $${\mathcal S}({\mathbb R})$$

Abstract: In this paper we investigate the spectra and the ergodic properties of the multiplication operators and the convolution operators acting on the Schwartz space $${\mathcal S}({\mathbb R})$$ S ( R ) of rapidly decreasing functions, i.e., operators of the form $$M_h: {\mathcal S}({\mathbb R})\rightarrow {\mathcal S}({\mathbb R})$$ M … Show more

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Cited by 7 publications
(3 citation statements)
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References 21 publications
(17 reference statements)
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“…For further results on mean ergodic operators we refer to [19,21]. For recent results on mean ergodic operators in lcHs' we refer to [1,2,3,4,5,6], for example, and the references therein.…”
Section: Preliminaries and The Action Of The Composition Operator Onmentioning
confidence: 99%
“…For further results on mean ergodic operators we refer to [19,21]. For recent results on mean ergodic operators in lcHs' we refer to [1,2,3,4,5,6], for example, and the references therein.…”
Section: Preliminaries and The Action Of The Composition Operator Onmentioning
confidence: 99%
“…For further results on mean ergodic operators we refer to [19,22]. For recent results on mean ergodic operators in lcHs' we refer to [1][2][3][4]7,12,17], for example, and the references therein.…”
Section: Preliminariesmentioning
confidence: 99%
“…The case of multiplication operators on weighted spaces of analytic functions on the complex unit disc was studied by Bonet and Ricker [11]. Albanese and the author in [5] have studied the spectra and the ergodic properties of the multiplication operators on the space S(R) of rapidly decreasing functions and the (PLB)-space of its multipliers. Echelon and co-echelon spaces were studied by Köthe and Toeplitz.…”
Section: Introductionmentioning
confidence: 99%