109 citations · 567 across the 25 of their papers we have counts for
4 papers · 1 filter
Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling
Johann S. Brauchart, Josef Dick, Lou Fang
In this paper we introduce a reproducing kernel Hilbert space defined on as the tensor product of a reproducing kernel defined on the unit sphere $\mathbb{S}^{d}…
Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces
Johann S. Brauchart, Josef Dick, Edward B. Saff +3
We prove that the covering radius of an -point subset of the unit sphere is bounded above by a power of the worst-case error for equal weight cubatur…
Distributing many points on spheres: minimal energy and designs
Johann S. Brauchart, Peter J. Grabner
This survey discusses recent developments in the context of spherical designs and minimal energy point configurations on spheres. The recent solution of the long standing problem o…
An Electrostatics Problem on the Sphere Arising from a Nearby Point Charge
Johann S. Brauchart, Peter D. Dragnev, Edward B. Saff
For a positively charged insulated d-dimensional sphere we investigate how the distribution of this charge is affected by proximity to a nearby positive or negative point charge wh…