Document Type

Presentation

Presentation Date

Summer 8-19-2015

Conference Name

10th Summer School in Potential Theory

Conference Location

Budapest, Hungary

Peer Review

Invited

Abstract

Minimal energy problems in the presence of external fields are a classic topic in logarithmic potential theory in the complex plane. Applications vary from asymptotics of orthogonal polynomials, to fast decreasing polynomials, to weighted polynomial and rational approximation, etc. Here we shall introduce the counterpart for measures supported on the unit sphere, with motivation arising from an application to separation results for minimal Riesz s-energy spherical configurations. A natural extension to axis-symmetric external fields is presented and separation results for minimal energy points with external fields. Finally, a work in progress report considers the special case s=d-2, where the external field is explicitly solved for discrete Riesz potential with mass points on the sphere and small enough charges at the mass points.

Keywords

Riesz potential, minimal energy, external fields

Disciplines

Analysis | Numerical Analysis and Computation | Other Physical Sciences and Mathematics

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