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  1. ; ; ; ; (, Concrete Operators)
    Abstract Previously, spectra of certain weighted composition operators W ѱ, φ on H 2 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 W ѱ, φ can be found when these maps exhibit both of the aforementioned properties, and we determine which symbols do so. 
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