Mercer's Condition

\int\!\int\! K(x,y)g(x)g(y)\,dx dy \geq 0.

EXAMPLES

The constant function
:

K(x, y)=1\,

satisfies Mercer's condition, as then the integral becomes by Fubini's Theorem
:

\int\!\int\! g(x)g(y)\,dx dy = \int\! g(x) \,dx \int\! g(y) \,dy = \left(\int\! g(x) \,dx
ight)^2

which is indeed Non-negative .

Information About