  In a general context of positive definite kernels $k$, we develop tools and
algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$
(RKHS). With reference to these RKHSs, our results allow inference from
samples; more precisely, reconstruction of an "entire" (or global) signal, a
function $f$ from $\mathscr{H}$, via generalized interpolation of $f$ from
partial information obtained from carefully chosen distributions of sample
points. We give necessary and sufficient conditions for configurations of
point-masses $\delta_{x}$ of sample-points $x$ to have finite norm relative to
the particular RKHS $\mathscr{H}$ considered. When this is the case, and the
kernel $k$ is given, we obtain an induced positive definite kernel
$\left\langle \delta_{x},\delta_{y}\right\rangle _{\mathscr{H}}$. We perform a
comparison, and we study when this induced positive definite kernel has $l^{2}$
rows and columns. The latter task is accomplished with the use of certain
symmetric pairs of operators in the two Hilbert spaces, $l^{2}$ on one side,
and the RKHS $\mathscr{H}$ on the other. A number of applications are given,
including to infinite network systems, to graph Laplacians, to resistance
metrics, and to sampling of Gaussian fields.
