论文标题
操作员重视积极的确定内核和可区分的普遍性
Operator valued positive definite kernels and differentiable universality
论文作者
论文摘要
我们提出了一个积极确定的运算符的表征，其有价值的内核是通用的或$ c_ {0} $ - 通用，并将这些特征应用于经营者家族的有价值核心，这些核心被证明表现得很好。稍后，我们为操作员获得了一个有价值的内核的特征，为$ c^{q} $ - undiville and $ c_ {0}^{q} $ - undiville。为了获得此类表征和示例，我们将有关可区分内核结构的一些众所周知的结果推广到操作员有价值的上下文。在示例中，请重点介绍欧几里得空间上的径向内核。
We present a characterization for a positive definite operator valued kernel to be universal or $C_{0}$-universal, and apply these characterizations to a family of operator valued kernels that are shown to be well behaved. Later, we obtain a characterization for an operator valued differentiable kernel to be $C^{q}$-universal and $C_{0}^{q}$-universal. In order to obtain such characterization and examples we generalize some well known results concerning the structure of differentiable kernels to the operator valued context. On the examples is given an emphasis on the radial kernels on Euclidean spaces.
