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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Detalles Bibliográficos
Autor: Bonet Solves, José Antonio|||0000-0002-9096-6380
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
Descripción
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.