Spectra of Weighted Composition Operators with Quadratic Symbols

IF 0.3 Q4 MATHEMATICS
Jessica Doctor, T. Hodges, Scott R. Kaschner, Alexander McFarland, D. Thompson
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引用次数: 0

Abstract

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.
二次符号加权复合算子的谱
先前,某些加权复合算子W , φ在H2上的谱是在以下两个假设之一下确定的:φ在所有的上而不是在紧子集上均匀收敛于Denjoy-Wolff点,或者φ是“本质线性分数”。我们证明了如果φ是一个抛物型的二次型自映射,那么当这些映射同时具有上述性质时,可以找到w, φ的谱,并确定了哪些符号具有上述性质。
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来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
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