Positive-definite kernel

Definition

Let

\{ H_n \}_{n \in {\mathbb Z}}

be a sequence of (complex) Hilbert spaces and

\mathcal{L}(H_i, H_j)

be the bounded operators from Hi to Hj.

A map A on {\mathbb Z} \times {\mathbb Z} where

A(i,j)\in\mathcal{L}(H_i, H_j)

is called a positive definite kernel if for all m > 0 and h_i \in H_i, the following non-negativity condition holds:

\sum_{-m \leq i\quad\, \atop j \leq m} \langle A(i,j) h_i, h_j \rangle \geq 0.


摘自：https://en.wikipedia.org/wiki/Positive-definite_kernel

bounded operator：http://www.encyclopediaofmath.org/index.php/Bounded_operator

posted on 2014-07-10 15:43  #hanhui  阅读(220)  评论(0)    收藏  举报