47 citations · 231 across the 47 of their papers we have counts for
6 papers · 1 filter
Next order energy asymptotics for Riesz potentials on flat tori
Douglas P. Hardin, Edward B. Saff, Brian Z. Simanek +1
Let be a lattice in with positive co-volume. Among -periodic -point configurations, we consider the minimal renormalized Riesz -energy $\mathcal{E}_{s,Λ}(N…
A Sharp Balian-Low Uncertainty Principle for Shift-Invariant Spaces
Douglas P. Hardin, Michael C. Northington V., Alexander M. Powell
A sharp version of the Balian-Low theorem is proven for the generators of finitely generated shift-invariant spaces. If generators are t…
Energy bounds for codes and designs in Hamming spaces
Peter G. Boyvalenkov, Peter D. Dragnev, Douglas P. Hardin +2
We obtain universal bounds on the energy of codes and for designs in Hamming spaces. Our bounds hold for a large class of potential functions, allow unified treatment, and can be v…
Universal upper and lower bounds on energy of spherical designs
P. G. Boyvalenkov, P. D. Dragnev, D. P. Hardin +2
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are vali…
Minimum Riesz energy problems for a condenser with "touching plates"
P. D. Dragnev, D. Hardin, E. B. Saff +1
Minimum Riesz energy problems in the presence of an external field are analyzed for a condenser with touching plates. We obtain sufficient and/or necessary conditions for the solva…
Universal lower bounds for potential energy of spherical codes
P. G. Boyvalenkov, P. D. Dragnev, D. P. Hardin +2
We derive and investigate lower bounds for the potential energy of finite spherical point sets (spherical codes). Our bounds are optimal in the following sense -- they cannot be im…