Reproducing Kernel Hilbert Spaces
Overview
Definition
Given a set {% X %} and the set of functions {% F(X, \mathbb{F}) %} from
{% X %} to {% \mathbb{F} %}, a subset {% H \subset F %} is a
Reproducing Kernel Hilbert Space if
- {% H %} is a vector space
- {% H %} has an
inner product
which makes {% H %} a
Hilbert Space
-
For any {% x \in X %}, the linear evaluation functional
{% E_x : H \rightarrow \mathbb{F} %} defined to be {% E_x(f) = f(x) %}
is bounded.
