A Reproducing Kernel Condition for Indeterminacy in the Multidimensional Moment Problem

使用再生核空间插值和模型降阶训练神经网络

Training Neural Networks Using Reproducing Kernel Space Interpolation and Model Reduction

本文提出利用再生核希尔伯特空间插值训练神经网络，推广至Krein空间，并基于多维AAK定理提出延长神经网络（PNN），在噪声环境中性能优于现有方法。

Scattering systems with several evolutions and formal reproducing kernel Hilbert spaces

A Schur-class function in $d$ variables is defined to be an analytic contractive-operator valued function on the unit polydisk. Such a function is said to be in the Schur--Agler class if it is contractive when evaluated on any commutative $d$-tuple of strict contractions on a Hilbert space. It is known that the Schur--Agler class is a strictly proper subclass of the Schur class if the number of variables $d$ is more than two. The Schur--Agler class is also characterized as those functions arising as the transfer function of a certain type (Givone--Roesser) of conservative multidimensional line…