1. Spectra of Weighted Composition Operators with Quadratic Symbols
- Author
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Doctor Jessica, Hodges Timothy, Kaschner Scott, McFarland Alexander, and Thompson Derek
- Subjects
uniform convergence ,essentially linear fractional ,composition operator ,weighted composition operator ,40a30 ,47b33 ,47b35 ,47a10 ,Mathematics ,QA1-939 - Abstract
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.
- Published
- 2022
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