Solution
= Solution
A symmetric function $k:\mathcal X^2\to\mathbb R$ is a <positive-definite kernel> when $\sum_{i,j}a_ia_jk(x_i,x_j)\geq0$ for every finite set of points and real coefficients. A <Reproducing-kernel Hilbert space> $\mathcal H$ is a Hilbert space of functions whose evaluation maps are continuous. Its reproducing kernel satisfies $k(x,\cdot)\in\mathcal H$ and $f(x)=\langle f,k(x,\cdot)\rangle_{\mathcal H}$.