Spectra of Weighted Composition Operators with Quadratic Symbols
Previously, spectra of certain weighted composition operators W ѱ, φ on H2 were determined under one of two hypotheses: either φ converges under iteration to the Denjoy-Wolff point uniformly on all of 𝔻 rather than simply on compact subsets, or φ is “essentially linear fractional.” We show that if φ...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-06-01
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| Series: | Concrete Operators |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/conop-2022-0129 |
| Summary: | Previously, spectra of certain weighted composition operators W ѱ, φ on H2 were determined under one of two hypotheses: either φ converges under iteration to the Denjoy-Wolff point uniformly on all of 𝔻 rather than simply on compact subsets, or φ is “essentially linear fractional.” We show that if φ is a quadratic self-map of 𝔻 of parabolic type, then the spectrum of Wѱ, φ can be found when these maps exhibit both of the aforementioned properties, and we determine which symbols do so. |
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| ISSN: | 2299-3282 |