Spectra of some weighted composition operators on H^2
Spectra of some weighted composition operators on H^2
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H^2 上一些加权合成算子的谱
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Feng Tian
中科院分区：
文献类型：
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作者：
C. Cowen;Eungil Ko;Derek Thompson;Feng Tian
我们完整地刻画了一个加权复合算子W ＿ψ， φ在$$H^2 (mathbb{D})$$上的谱，当φ具有Denjoy-Wolff点a且φ < 0 < | ϕ ‘ (a)| < 1时，迭代，φ ＿n均匀收敛于a，并且ψ在H ^∞（$$mathbb{D}$$上的有界解析函数空间）中连续且在a处连续。我们还给出了当| a | = 1且φ ’ (a) = 1时的界和一些计算，此外，证明这些符号包括所有线性分数φ是双曲和抛物非自同构。最后，我们使用这些结果来消除可能的权重ψ，使W ＿ψ， φ是半正规的。
We completely characterize the spectrum of a weighted composition operator W _ψ, ϕ on $$H^2 (mathbb{D})$$ when ϕ has Denjoy–Wolff point a with 0 < | ϕ ′( a )| < 1, the iterates, ϕ _n, converge uniformly to a , and ψ is in H ^∞ (the space of bounded analytic functions on $$mathbb{D}$$ ) and continuous at a. We also give bounds and some computations when | a | = 1 and ϕ ′( a ) = 1 and, in addition, show that these symbols include all linear fractional ϕ that are hyperbolic and parabolic nonautomorphisms. Finally, we use these results to eliminate possible weights ψ so that W _ψ, ϕ is seminormal.