Spectrum of invertible weighted composition operators on the unit disk
Oliva-Maza, Jesús (Universidad de Zaragoza)
Resumen: The spectrum of invertible weighted composition operators acting on classical Banach spaces of holomorphic functions in the unit disk has been studied intensively over the years. Complete descriptions of that spectrum have been given in the elliptic or parabolic cases, that is, for φ either elliptic or parabolic, but only partial results have been obtained in the remaining case, that is, for hyperbolic φ. In this paper, we give the spectrum and the essential spectrum of for hyperbolic φ. Our results answer in the positive several conjectures posed by different authors.
In order to deal with the above questions, we present new techniques which involve the embedding of the weight u into a cocycle associated to an hyperbolic flow . We also provide information about the range spaces and null spaces of for λ lying in the interior of .
Idioma: Inglés
DOI: 10.1016/j.jfa.2025.111186
Año: 2025
Publicado en: JOURNAL OF FUNCTIONAL ANALYSIS 290, 1 (2025), 111186 [43 pp.]
ISSN: 0022-1236
Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-23R
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2022-137294NB-I00
Tipo y forma: Article (Published version)
Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes.
Exportado de SIDERAL (2025-10-17-14:22:01)
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In order to deal with the above questions, we present new techniques which involve the embedding of the weight u into a cocycle associated to an hyperbolic flow . We also provide information about the range spaces and null spaces of for λ lying in the interior of .
Idioma: Inglés
DOI: 10.1016/j.jfa.2025.111186
Año: 2025
Publicado en: JOURNAL OF FUNCTIONAL ANALYSIS 290, 1 (2025), 111186 [43 pp.]
ISSN: 0022-1236
Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-23R
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2022-137294NB-I00
Tipo y forma: Article (Published version)
Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. Exportado de SIDERAL (2025-10-17-14:22:01)
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Record created 2025-09-19, last modified 2025-10-17