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Utilizing frameworks developed by Delsarte, Yudin and Levenshtein, we deduce linear programming lower bounds (as    N  →  ∞   ) 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  |    −  swith    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  (  −  α  |  x  −  y   |  2   )    on    R  p   , we obtain lower bounds for the energy of infinite configurations having a prescribed density.

ASYMPTOTIC LINEAR PROGRAMMING LOWER BOUNDS FOR THE ENERGY OF MINIMIZING RIESZ AND GAUSS CONFIGURATIONS