论文标题
在几个变量的特征函数的确定性属性上
On the deterministic property for characteristic functions of several variables
论文作者
论文摘要
假设$ f $是$ r^n $上的概率度量$μ_f$的特征函数。令$σ> 0 $。我们研究以下推出问题：在无限$v_σ= \ {x \ in r^n：| | x_k |>σ，\ k = 1，\ dots，n \} $ in $ r^n $中是否存在$ r^n $上的特征g $ g $ v_ v $ g g g g $ g g $，但是令$μ_f$具有无零的零件，其中连续密度$φ$。在本文中，给出了$φ$的某些足够条件，并给出了$v_σ$，后者的问题具有肯定的答案。我们还解决了这些条件的最佳性。我们的结果表明，不仅$v_σ$的大小和支持$ {\ text {\，supp} \，}φ$都有$ {\ text {\ text {\，supp} \，}φ$的某些算术属性。
Assume that $f$ is the characteristic function of a probability measure $μ_f$ on $R^n$. Let $σ>0$. We study the following extrapolation problem: under what conditions on the neighborhood of infinity $V_σ=\{x\in R^n: |x_k|>σ, \ k=1,\dots, n\}$ in $R^n$ does there exist a characteristic function $g$ on $R^n$ such that $g=f$ on $V_σ$, but $g\not\equiv f$? Let $μ_f$ have a nonzero absolutely continuous part with continuous density $φ$. In this paper certain sufficient conditions on $φ$ and $V_σ$ are given under which the latter question has an affirmative answer. We also address the optimality of these conditions. Our results indicate that not only does the size of both $V_σ$ and the support ${\text{\,supp}\,}φ$ matter, but also certain arithmetic properties of ${\text{\,supp}\,}φ$.
