4 papers · 1 filter
Energy, Polarization, and Separation of Greedy Sequences for Riesz and Green Kernels
Dmitriy Bilyk, Liudmyla Kryvonos, Ryan W. Matzke +1
We investigate the asymptotic behavior of greedy -Riesz and Green energy sequences on the unit sphere , where…
On the lower bounds for the spherical cap discrepancy
Dmitriy Bilyk, Johann S. Brauchart
We start by providing a very simple and elementary new proof of the classical bound due to J. Beck which states that the spherical cap -discrepancy of any points…
Positive definite singular kernels on two-point homogeneous spaces
Dmitriy Bilyk, Peter Grabner
We study positive definiteness of kernels on two-point homogeneous spaces. As opposed to the classical case, which has been developed and studied in the existing literatur…
Geodesic Distance Riesz Energy on Projective Spaces
Dmitriy Bilyk, Ryan W. Matzke, Joel Nathe
We study probability measures that minimize the Riesz energy with respect to the geodesic distance on projective spaces (such energies arise from…