球上积空间、转向带和随机场上的Rudin扩张定理
Rudin Extension Theorems on Product Spaces, Turning Bands, and Random Fields on Balls cross Time
摘要：
径向对称的特征函数具有双重解释，因为它们可以用作空间随机场的各向同性相关函数。从球到$d$维欧氏空间的各向同性相关函数的扩展$\R^{d}$在Rudin之后已经被理解。然而，积空间上的扩张定理是难以捉摸的，并且Rudin在矩形上提供的一个反例表明该问题是相当具有挑战性的。本文对任意两个正整数$d$和$\dd$，给出了定义在嵌入$\R^d$十字的球（$\R^{\dd}$或嵌入$\R^{\dd+1}$的单位球$§^{\dd}$）中的多径向特征函数的扩张定理.然后，我们研究转向带运营商，提供双射类之间的多径向相关函数在给定的积空间，和多径向相关的积空间具有不同的尺寸。延伸定理与转向带的结合提供了一种与定义在球穿过线性或圆形时间中的随机场的联系。
英文摘要：
Characteristic functions that are radially symmetric have a dual interpretation, as they can be used as the isotropic correlation functions of spatial random fields. Extensions of isotropic correlation functions from balls into $d$-dimensional Euclidean spaces, $\R^{d}$, have been understood after Rudin. Yet, extension theorems on product spaces are elusive, and a counterexample provided by Rudin on rectangles suggest that the problem is quite challenging. This paper provides extension theorem for multiradial characteristic functions that are defined in balls embedded in $\R^d$ cross, either $\R^{\dd}$ or the unit sphere $§^{\dd}$ embedded in $\R^{\dd+1}$, for any two positive integers $d$ and $\dd$. We then examine Turning Bands operators that provide bijections between the class of multiradial correlation functions in given product spaces, and multiradial correlations in product spaces having different dimensions. The combination of extension theorems with Turning Bands provides a connection with random fields that are defined in balls cross linear or circular time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
