论文标题
Quaternionic阳性在Abelian群体上的凸特征
convex characteristics of quaternionic positive definite functions on abelian groups
论文作者
论文摘要
本文涉及归一化四基因值的正定阳性功能的拓扑空间，尤其是其凸特性。有两个主要结果。首先，我们证明，此类功能家族中的极端要素正是从G到Sphere s的同态，即四元组代数中的3个单位。其次，我们真正的现象是在复杂的环境中不存在的现象：这种功能的紧凑型凸集不是鲍尔单纯形，除非g的指数小于或等于2。我们还提出了用于应用程序和其他一些次要有趣结果的功能的积分表示。
This paper is concerned with the topological space of normalized quaternion-valued positive definite functions on an arbitrary abelian group G, especially its convex characteristics. There are two main results. Firstly, we prove that the extreme elements in the family of such functions are exactly the homomorphisms from G to the sphere group S, i.e., the unit 3-sphere in the quaternion algebra. Secondly, we real a phenomenon which does not exist in the complex setting: The compact convex set of such functions is not a Bauer simplex except when G is of exponent less than or equal to 2. In contrast, its complex counterpart is always a Bauer simplex, as is well known. We also present an integral representation for such functions as an application and some other minor interesting results.
