论文标题
Rudin扩展定理在产品空间上，转带和球上的随机字段交叉时间
Rudin Extension Theorems on Product Spaces, Turning Bands, and Random Fields on Balls cross Time
论文作者
论文摘要
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。在鲁丁之后，已经理解了各向同性相关功能从球到$ d $ d $二维的欧几里得空间，$ \ r^{d} $的扩展。然而，产品空间上的扩展定理难以捉摸，鲁丁在矩形上提供的反例表明，问题很具有挑战性。本文提供了用于多次特征函数的扩展定理，这些函数定义在$ \ r^d $ cross中的球中，$ \ r^{\ dd} $或单位球$§^{\ dd} $ embedd in $ \ r^{\ r^{\ dd+1} $，对于$ dd $ dd $ dd $ dd $ dd $ dd $ dd $ dd $ dd $ d。然后，我们检查了转弯带操作员，这些操作员在给定的产品空间中提供了多个多次相关函数的射之间，以及具有不同维度的产品空间中的多次关系相关性。延伸定理与转谱带的组合提供了与在球交叉线性或圆形时间中定义的随机场的连接。
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.
