二阶再生张量空间与再生张量的性质

Reproducing Second-order Tensor Space and Properties of Reproducing Tensors

将二阶张量借以线性空间的方式来描述,进而在此建立泛函分析的内积、范数等结构,将再生核概念引入到张量空间中去.证明了四阶再生张量是二阶张量空间的再生核.再生张量的唯一性以及其他属性依次给予证明.

In this paper, a second-order tensor as a linear space is proposed to describe and the inner product and norms in the functional analysis is proceeded to construct by introducing the concept of reproducing Kernel into tensor spaces. The research demonstrates that a tensor of Order 4 is a reproducing Kernel of a second-order tensor space. Additionally, the uniqueness of the reproducing tensors and other properties are examined.