We show that convolution operators on certain spaces of entire functions of a given type and order on Banach spaces are strongly mixing with respect to an invariant Borel probability measure with full support (a stronger property than frequent hypercyclicity). Based on results of S. Muro, D. Pinasco and M. Savransky we also show the existence of frequently hypercyclic entire functions of exponential growth, and the existence of frequently hypercyclic subspaces for such convolution operators.

中文翻译：

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给定类型和阶次的整个函数的 Fréchet 空间上的强混合卷积算子

我们表明，在 Banach 空间上给定类型和阶数的整个函数的某些空间上的卷积算子与具有完全支持的不变 Borel 概率度量（比频繁的超循环性更强的属性）强烈混合。基于 S. Muro、D. Pinasco 和 M. Savransky 的结果，我们还展示了指数增长的频繁超循环全函数的存在，以及此类卷积算子的频繁超循环子空间的存在。