3 citations · 3 across the 4 of their papers we have counts for
6 papers
Optimal Measures for Multivariate Geometric Potentials
Dmitriy Bilyk, Damir Ferizović, Alexey Glazyrin +3
We study measures and point configurations optimizing energies based on multivariate potentials. The emphasis is put on potentials defined by geometric characteristics of sets of p…
Optimizers of three-point energies and nearly orthogonal sets
Dmitriy Bilyk, Damir Ferizović, Alexey Glazyrin +3
This paper is devoted to spherical measures and point configurations optimizing three-point energies. Our main goal is to extend the classic optimization problems based on pairs of…
Positive definiteness and the Stolarsky invariance principle
Dmitriy Bilyk, Ryan Matzke, Oleksandr Vlasiuk
In this paper we elaborate on the interplay between energy optimization, positive definiteness, and discrepancy. In particular, assuming the existence of a -invariant measure $μ…
Potential theory with multivariate kernels
Dmitriy Bilyk, Damir Ferizović, Alexey Glazyrin +3
In the present paper we develop the theory of minimization for energies with multivariate kernels, i.e. energies, in which pairwise interactions are replaced by interactions betwee…
Energy on spheres and discreteness of minimizing measures
Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke +2
In the present paper we study the minimization of energy integrals on the sphere with a focus on an interesting clustering phenomenon: for certain types of potentials, optimal meas…
Optimal measures for p-frame energies on spheres
Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke +2
We provide new answers about the placement of mass on spheres so as to minimize energies of pairwise interactions. We find optimal measures for the -frame energies, i.e. energie…