4 papers
Universal polar dual pairs of spherical codes found in and
S. V. Borodachov, P. G. Boyvalenkov, P. D. Dragnev +3
We identify universal polar dual pairs of spherical codes and such that for a large class of potential functions the minima of the discrete -potential of on the…
Bounds on Discrete Potentials of Spherical (k,k)-Designs
S. Borodachov, P. Boyvalenkov, P. Dragnev. D. Hardin. E. Saff +1
We derive universal lower and upper bounds for max-min and min-max problems (also known as polarization) for the potential of spherical -designs and provide certain examples…
Energy bounds for weighted spherical codes and designs via linear programming
Sergiy Borodachov, Peter Boyvalenkov, Peter Dragnev +3
Universal bounds for the potential energy of weighted spherical codes are obtained by linear programming. The universality is in the sense of Cohn-Kumar -- every attaining code is…
Bounds on energy and potentials of discrete measures on the sphere
S. Borodachov, P. Boyvalenkov, P. Dragnev +3
We establish upper and lower universal bounds for potentials of weighted designs on the sphere that depend only on quadrature nodes and weights derived from the…