Fernández Rosell, C.; Galbis Verdu, A.; Jorda Mora, E. (2018). Dynamics and spectra of composition operators on the Schwartz space. Journal of Functional Analysis. 274(12):3503-3530. https://doi.org/10.1016/j.jfa.2017.11.005
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/124315
Title:
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Dynamics and spectra of composition operators on the Schwartz space
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Author:
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FERNÁNDEZ ROSELL, CARMEN
GALBIS VERDU, ANTONIO
Jorda Mora, Enrique
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UPV Unit:
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Universitat Politècnica de València. Instituto Universitario de Matemática Pura y Aplicada - Institut Universitari de Matemàtica Pura i Aplicada
Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
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Issued date:
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Abstract:
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[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 ...[+]
[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.
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Subjects:
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Space of rapidly decreasing functions
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Mean ergodic composition operator
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Power bounded operator
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Spectrum
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Copyrigths:
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Reserva de todos los derechos
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Source:
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Journal of Functional Analysis. (issn:
0022-1236
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DOI:
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10.1016/j.jfa.2017.11.005
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Publisher:
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Elsevier
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Publisher version:
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https://doi.org/10.1016/j.jfa.2017.11.005
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Project ID:
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info:eu-repo/grantAgreement/MINECO//MTM2016-76647-P/ES/ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y ANALISIS TIEMPO-FRECUENCIA/
info:eu-repo/grantAgreement/GVA//AICO%2F2016%2F054/
info:eu-repo/grantAgreement/GVA//PROMETEO%2F2017%2F102/ES/ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONES/
info:eu-repo/grantAgreement/GVA//ACOMP%2F2015%2F186/
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Thanks:
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The present research was partially supported by the projects MTM2016-76647-P, ACOMP/2015/186, Prometeo/2017/102 of the Generalitat Valenciana (Spain). The third author was partially supported by GVA, Project AICO/2016/054.[+]
The present research was partially supported by the projects MTM2016-76647-P, ACOMP/2015/186, Prometeo/2017/102 of the Generalitat Valenciana (Spain). The third author was partially supported by GVA, Project AICO/2016/054.
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Type:
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Artículo
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