具有再生核的多元整函数空间上平移算子与微分算子的关系

The Relationship between Translation operators and Differentiation operators on the Entire Function Spaces of Several Complex Variables with Reproducing kernel

在具有再生核函数的多元整函数Hilbert空间中讨论了平移算子与微分算子之间的关系,从而推广了Chan和Shapiro等在文[1]中的结果,为讨论该空间上平移算子的循环性以及不变子空间问题提供了必要的条件。

In this paper,we discuss the relationship of translation operators and differentiation operators on the entire function spaces of several complex variables with reproducing kernel,thus we generalized the result of Chan and Shapiro in [1],and provide the necessary conditions for the discussion of cyclicity of translation operators and the invariant subspace problem on the spaces.