前言

這個筆記是北大那位老師課程的學習筆記，講的概念淺顯易懂，非常有利於我們掌握基本的概念，從而掌握相關的技術。

basic concepts

If a function is positive definite，then matrix is P.S.D. ${x_1,,,,x_n} \subset X => K_0(x_i,x_j)=g(x_i)g(x_j)$ $=\>k_0=\left[g\right(x_1),\mathrm{.}\mathrm{.},g(x_n){]}^{\mathrm{\prime }}\ast [g($

Thm:

Let F be a probalility measure on the half low Pat such that $0< \int _0^{\infin} s dF(s)<\infin$ and l(F,u)=${\int }_0^{\mathrm{\infty }}exp$

Levy distribution

$(B\mathrm{/}2\ast$

Thm

let $k X*X -> R$ be a P.D kernel then exists a HILBERT space H and from x->H such that $\phi(H)$ $\forall x,y \subset x,K(x,y)=<\phi(x),\phi(y)>$ three kernels.