距离空间中的向量值伪概周期函数

Vector-valued pseudo almost periodic functions in metric spaces

定义了距离空间中的向量值伪概周期函数,考察了该函数的性质.这类向量值函数包含了一些已知函数作为特殊情况(例如概周期函数,渐近概周期函数等).应用数学分析中的基本方法证明了唯一分解定理,即距离空间中的向量值伪概周期函数和概周期函数之间的距离是一个遍历扰动.

Vector- valued pseudo almost periodic functions in metric spaces are defined, and their properties are investigated. The vector- valued functions contain many known functions as special cases, such as almost periodic functions, asymptotically almost periodic functions and so on. Some fundamental methods in mathematical analysis are applied to prove the unique decomposition theorem ： the distance between vector - valued pseudo almost periodic functions in metric spaces and almost periodic functions is an ergodic perturbation.