Spectrum of composition operators on S(R) with polynomial symbols
[EN] We study the spectrum of operators in the Schwartz space of rapidly decreasing functions which associate each function with its composition with a polynomial. In the case where this operator is mean ergodic we prove that its spectrum reduces to {0}, while the spectrum of any non mean ergodic co...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2020 |
| Country: | España |
| Institution: | Universitat Politècnica de València (UPV) |
| Repository: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Language: | English |
| OAI Identifier: | oai:riunet.upv.es:10251/166135 |
| Online Access: | https://riunet.upv.es/handle/10251/166135 |
| Access Level: | Open access |
| Keyword: | Composition operator Space of rapidly decreasing functions Spectrum Mean ergodic operator MATEMATICA APLICADA |
| Summary: | [EN] We study the spectrum of operators in the Schwartz space of rapidly decreasing functions which associate each function with its composition with a polynomial. In the case where this operator is mean ergodic we prove that its spectrum reduces to {0}, while the spectrum of any non mean ergodic composition operator with a polynomial always contains the closed unit disc except perhaps the origin. We obtain a complete description of the spectrum of the composition operator with a quadratic polynomial or a cubic polynomial with positive leading coefficient. |
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