Towards spectral descriptions of cyclic functions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912197642289152 |
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| author | Monsalve, Miguel Seco, Daniel |
| author_facet | Monsalve, Miguel Seco, Daniel |
| contents | 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 $H^2_ω$ of the function $z \mapsto a-z$ can be inferred from the spectral properties of analogous operators $V_a$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12298 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards spectral descriptions of cyclic functions Monsalve, Miguel Seco, Daniel Functional Analysis Classical Analysis and ODEs Complex Variables Primary: 47B32, Secondary: 30J05, 47A10, 47A16 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 $H^2_ω$ of the function $z \mapsto a-z$ can be inferred from the spectral properties of analogous operators $V_a$. 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. |
| title | Towards spectral descriptions of cyclic functions |
| topic | Functional Analysis Classical Analysis and ODEs Complex Variables Primary: 47B32, Secondary: 30J05, 47A10, 47A16 |
| url | https://arxiv.org/abs/2501.12298 |