24 citations · 79 across the 31 of their papers we have counts for
33 papers
On Constrained Riesz Minimum Energy Problems
Dan Coroian, Peter Dragnev, Alan Legg +1
The constrained equilibrium problem for the logarithmic potential was introduced by Rakhmanov (1996) as he realized that the asymptotic distribution of the zeros of discrete orthog…
Universal polar dual pairs]{Universal polar dual pairs of spherical codes found in and the Leech lattice
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…
Riesz equilibrium on a ball in the external field of a point charge
Peter D. Dragnev, Ramon Orive, Eduard B. Saff +1
We investigate the Riesz energy minimization problem on a -dimensional ball in the presence of an external field created by a point charge above the ball in , …
Universal optimality of -avoiding spherical codes and designs
P. G. Boyvalenkov, D. D. Cherkashin, P. D. Dragnev
Given an open set , we introduce the concepts of -avoiding spherical codes and designs, that is, spherical codes that have no inner products in the set . We…
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…
Universal minima of discrete potentials for sharp spherical codes
Peter Boyvalenkov, Peter Dragnev, Douglas Hardin +2
This article is devoted to the study of discrete potentials on the sphere in for sharp codes. We show that the potentials of most of the known sharp codes attain the…
On polarization of spherical codes and designs
Peter Boyvalenkov, Peter Dragnev, Douglas Hardin +2
In this article we investigate the -point min-max and the max-min polarization problems on the sphere for a large class of potentials in . We derive universal lowe…
Point Source Equilibrium Problems with Connections to Weighted Quadrature Domains
Peter D. Dragnev, Alan R. Legg, Edward B. Saff
We explore the connection between supports of equilibrium measures and quadrature identities, especially in the case of point sources added to the external field wi…
Riesz energy problems with external fields and related theory
Peter Dragnev, Ramon Orive, Edward B. Saff +1
In this paper, we investigate Riesz energy problems on unbounded conductors in in the presence of general external fields , not necessarily satisfying the growth conditio…
On the Best Uniform Polynomial Approximation to the Checkmark Function
Peter D. Dragnev, Alan R. Legg, Ramon Orive
The best uniform polynomial approximation of the checkmark function is considered, as varies in . For each fixed degree , the minimax error is…
Logarithmic Equilibrium on the Sphere in the Presence of Multiple Point Charges
A. R. Legg, P. D. Dragnev
With the sphere as a conductor holding a unit charge with logarithmic interactions, we consider the problem of determining the support of the eq…
Universal Bounds for Size and Energy of Codes of Given Minimum and Maximum Distances
Peter Boyvalenkov, Peter Dragnev, Douglas Hardin +2
We employ signed measures that are positive definite up to certain degrees to establish Levenshtein-type upper bounds on the cardinality of codes with given minimum and maximum dis…
Log-optimal (d+2)-configurations in d-dimensions
Peter D. Dragnev, Oleg R. Musin
We enumerate and classify all stationary logarithmic configurations of d+2 points on the unit (d-1)-sphere in d-dimensions. In particular, we show that the logarithmic energy attai…
Upper bounds for energies of spherical codes of given cardinality and separation
Peter Boyvalenkov, Peter Dragnev, Douglas Hardin +2
We introduce a linear programming framework for obtaining upper bounds for the potential energy of spherical codes of fixed cardinality and minimum distance. Using Hermite interpol…
Universal bounds for spherical codes: the Levenshtein framework lifted
Peter Boyvalenkov, Peter Dragnev, Douglas Hardin +2
Based on the Delsarte-Yudin linear programming approach, we extend Levenshtein's framework to obtain lower bounds for the minimum -energy of spherical codes of prescribed dimens…
On point-mass Riesz external fields on the real axis
David Benko, Peter Dragnev, Ramon Orive
The purpose of this work is twofold. First, we aim to extend for the results of one of the authors about equilibrium measures in the real axis in external fields created by…
Energy Bounds for Codes in Polynomial Metric Spaces
Peter Boyvalenkov, Peter Dragnev, Douglas Hardin +2
In this article we present a unified treatment for obtaining bounds on the potential energy of codes in the general context of polynomial metric spaces (PM-spaces). The lower bound…
On spherical codes with inner products in a prescribed interval
P. G. Boyvalenkov, P. D. Dragnev, D. P. Hardin +2
We develop a framework for obtaining linear programming bounds for spherical codes whose inner products belong to a prescribed subinterval of . An intricate rela…
Condensers with touching plates and constrained minimum Riesz and Green energy problems
P. D. Dragnev, B. Fuglede, D. P. Hardin +2
We study minimum energy problems relative to the -Riesz kernel , , over signed Radon measures on , , associated with a gene…
Constrained minimum Riesz energy problems for a condenser with intersecting plates
P. D. Dragnev, B. Fuglede, D. P. Hardin +2
We study the constrained minimum energy problem with an external field relative to the -Riesz kernel of order for a generalized condenser $\mathbf A=(A…
Logarithmic and Riesz Equilibrium for Multiple Sources on the Sphere --- the Exceptional Case
Johann S. Brauchart, Peter D. Dragnev, Edward B. Saff +1
We consider the minimal discrete and continuous energy problems on the unit sphere in the Euclidean space in the presence of an external field due…
Probability, Minimax Approximation and Nash-Equilibrium. Estimating the Parameter of a Biased Coin
D. Benko, D. Coroian, P. D. Dragnev +1
This paper deals with the application of Approximation Theory type techniques to study a classical problem in Probability: estimating the parameter of a biased coin. For this purpo…
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…