2 papers
math.CA2021
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…
math.CA2019
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…