正则性和正定性的传播：一种建设性的方法
Propagation of regularity and positive definiteness: a constructive approach
摘要：
我们证明了，对于正定核，如果特定形式的正则性（连续性，Sn-可微性或全纯性）保持局部的对角线上，那么它们必须保持全局的正定性的整个域。这种局部到全局传播的规律性建设性地示出的后果的代数结构所引起的相关的双线性型的非负性高达5阶。这些结果的后果拓扑群和正定和指数凸函数进行了探讨。
英文摘要：
We show that, for positive definite kernels, if specific forms of regularity (continuity, Sn-differentiability or holomorphy) hold locally on the diagonal, then they must hold globally on the whole domain of positive-definiteness. This local-to-global propagation of regularity is constructively shown to be a consequence of the algebraic structure induced by the non-negativity of the associated bilinear forms up to order 5. Consequences of these results for topological groups and for positive definite and exponentially convex functions are explored.
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。
