Given an affine symbol \(\varphi \) and a multiplier w, we focus on the weighted composition operator \(C_{w, \varphi }\) acting on the spaces Exp and \(Exp^0\) of entire functions of exponential and of infraexponential type, respectively. We characterize the continuity of the operator and, for w the product of a polynomial by an exponential function, we completely characterize power boundedness and (uniform) mean ergodicity. In the case of multiples of composition operators, we also obtain the spectrum and characterize hypercyclicity.

中文翻译：

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指数型和亚指数型全函数空间上加权复合算子的动力学

给定一个仿射符号\(\varphi \)和一个乘数w，我们关注加权合成算子\(C_{w, \varphi }\)作用于整个函数的空间Exp和\(Exp^0\)分别是指数型和指数型。我们表征操作的连续性，并为w ^的指数函数多项式的产品，我们的完全刻画功率和有界性（均匀）的平均遍历性。在复合算子的倍数的情况下，我们还获得了频谱并表征了​​超循环。