Towards spectral descriptions of cyclic functions
We build on a characterization of inner functions $f$ due to Le, in terms of the spectral properties of the operator $V = M_f^*M_f$ and study to what extent the cyclicity on weighted Hardy spaces $H^2$ of the function $z \mapsto a − z$ can be similarly inferred from the spectral properties of the co...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2025 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositório: | Docta Complutense |
| Idioma: | inglês |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/128676 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/128676 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Inner functions Cyclic functions Multiplication operators Reproducing kernel Hilbert spaces Point spectrum Análisis funcional y teoría de operadores 1202.14 Espacio de Hilbert 1202.09 Funciones de Una Variable Compleja |
| Resumo: | We build on a characterization of inner functions $f$ due to Le, in terms of the spectral properties of the operator $V = M_f^*M_f$ and study to what extent the cyclicity on weighted Hardy spaces $H^2$ of the function $z \mapsto a − z$ can be similarly inferred from the spectral properties of the corresponding operator $V$. We describe several properties of the spectra that hold in a large class of spaces and then, we focus on the particular case of Bergman-type spaces, for which we describe completely the spectrum of such operators and find all eigenfunctions. |
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