A note about the spectrum of composition operators induced by a rotation
[EN] A characterization of those points of the unit circle which belong to the spectrum of a composition operator C phi, defined by a rotation phi (z)=rz with |r|=1, on the space H0(D) of all analytic functions which vanish at 0, is given. Examples show that the spectrum of C phi need not be closed....
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/162570 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/162570 |
| Access Level: | acceso abierto |
| Palabra clave: | Composition operator Space of analytic functions Rotation Diophantine number MATEMATICA APLICADA |
| Sumario: | [EN] A characterization of those points of the unit circle which belong to the spectrum of a composition operator C phi, defined by a rotation phi (z)=rz with |r|=1, on the space H0(D) of all analytic functions which vanish at 0, is given. Examples show that the spectrum of C phi need not be closed. In these examples the spectrum is dense but point 1 may or may not belong to it, and this is related to Diophantine approximation. |
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