Potential theory with multivariate kernels

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

*Korrespondierende/r Autor/-in für diese Arbeit

Publikation: ArbeitspapierWorking paper


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.
PublikationsstatusEingereicht - 9 Apr. 2021

ASJC Scopus subject areas

  • Analyse


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