  Utilizing frameworks developed by Delsarte, Yudin and Levenshtein, we deduce
linear programming lower bounds (as $N\to \infty$) for the Riesz energy of
$N$-point configurations on the $d$-dimensional unit sphere in the so-called
hypersingular case; i.e, for non-integrable Riesz kernels of the form
$|x-y|^{-s}$ with $s>d.$ As a consequence, we immediately get (thanks to the
Poppy-seed bagel theorem) lower estimates for the large $N$ limits of minimal
hypersingular Riesz energy on compact $d$-rectifiable sets. Furthermore, for
the Gaussian potential $\exp(-\alpha|x-y|^2)$ on $\mathbb{R}^p,$ we obtain
lower bounds for the energy of infinite configurations having a prescribed
density.
