6 Reproducing-kernel Hilbert spaces

Background conventions: the Mathlib class RKHS ℝ H X ℝ is the scalar-valued reproducing-kernel Hilbert space on a domain \(X\), with Hilbert space \(\mathcal{H}= H\) and feature map \(k_x := \mathrm{kerFun}\, H\, x\, 1 \in H\) satisfying \(f(x) = \langle k_x, f \rangle \) [ 1 ] . Throughout, \(\mathcal{H}\) denotes a complete, separable, real inner product space.