论文标题
通过Gelfand对的时空协方差函数的统一视图
A unified view of space-time covariance functions through Gelfand pairs
论文作者
论文摘要
我们在两个Gelfand对的乘积上给出了正面确定的集成函数的表征，这是Gelfand对的一个正定函数在另一个Gelfand Pair上的Plancherel测度上的一个积极函数的组成部分。 在特殊的情况下，Gelfand对是欧几里得组，并且紧凑的亚组降低为身份，由于Cressie，Huang和Gneiting导致时空统计，表征是众多引用的结果。 当Gelfand对之一紧凑时，表征会导致有关具有正定扩展功能的球形函数扩展的结果，从而与Peron和Percu合作恢复了作者的最新结果。在特殊情况下，紧凑的gelfand对由正交组组成时，表征在地统计学中很重要，并且涵盖了porcu和white的最新结果。
We give a characterization of positive definite integrable functions on a product of two Gelfand pairs as an integral of positive definite functions on one of the Gelfand pairs with respect to the Plancherel measure on the dual of the other Gelfand pair. In the very special case where the Gelfand pairs are Euclidean groups and the compact subgroups are reduced to the identity, the characterization is a much cited result in spatio-temporal statistics due to Cressie, Huang and Gneiting. When one of the Gelfand pairs is compact the characterization leads to results about expansions in spherical functions with positive definite expansion functions, thereby recovering recent results of the author in collaboration with Peron and Porcu. In the special case when the compact Gelfand pair consists of orthogonal groups, the characterization is important in geostatistics and covers a recent result of Porcu and White.
