Bounded weighted composition operators, as well as compact weighted composition operators, on Fock spaces have been characterised. This characterisation is refined in terms of the order and type of the multiplier, and a complete description of zero-free multipliers is obtained. Explicit asymptotics for iterates of such operators are given. As an application, the question of whether weighted composition operators on the Fock space can be supercyclic is answered in the negative.

中文翻译：

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Fock空间上的加权合成算子及其动力学

Fock空间上的有界加权合成算子和紧凑加权合成算子已被表征。根据乘法器的顺序和类型对特征进行了细化，并获得了无零乘法器的完整描述。给出了此类算子迭代的显式渐近性。作为应用，在Fock空间上的加权合成算符是否可以是超循环的问题得到了否定的答案。