Potential theory with multivariate kernels

Damir Ferizović, Dmitriy Bilyk*, Ryan Matzke, Josiah Park, Alexey Glazyrin, Oleksandr Vlasiuk

*Korrespondierende/r Autor/in für diese Arbeit

Publikation: ArbeitspapierWorking paper

Abstract

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 between triples or, more generally, n-tuples of particles. Such objects, which arise naturally in various fields, present subtle differences and complications when compared to the classical two-input case. We introduce appropriate analogues of conditionally positive definite kernels, establish a series of relevant results in potential theory, explore rotationally invariant energies on the sphere, and present a variety of interesting examples, in particular, some optimization problems in probabilistic geometry which are related to multivariate versions of the Riesz energies.
Originalspracheenglisch
Seitenumfang23
PublikationsstatusEingereicht - 9 Apr 2021

ASJC Scopus subject areas

  • Analyse

Fingerprint

Untersuchen Sie die Forschungsthemen von „Potential theory with multivariate kernels“. Zusammen bilden sie einen einzigartigen Fingerprint.

Dieses zitieren