Mikhail SODIN

✬
Normalization:
The functions fL are normalized if Ef 2 L (x) = KL(x, x) = 1, x ∈ X.
Wlog, we assume that the functions fL are normalized.
Otherwise, replace the functions fL and the kernel KL by
✫
fL(x) = fL(x)
Ef 2 L (x) , KL(x, y) =
KL(x, y)
KL(x, x) · KL(y, y) .
This normalization changes the Hilbert spaces HL but the zero sets of
the Gaussian functions fL and fL remain the same.
In basic examples, the function x ↦→ KL(x, x) is constant (that is, the
norm of the point evaluation in HL does not depend on the point), so the
normalization boils down to computation of that constant.
9
✩
✪