Potential theory with multivariate kernels

Authors

Dmitriy Bilyk
Damir Ferizović
Alexey Glazyrin, The University of Texas Rio Grande Valley
Ryan Matzke
Josiah Park
Oleksandr Vlasiuk

Document Type

Article

Publication Date

3-15-2022

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.

Comments

© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature

Recommended Citation

Bilyk, D., Ferizović, D., Glazyrin, A. et al. Potential theory with multivariate kernels. Math. Z. (2022). https://doi.org/10.1007/s00209-022-03000-z

Publication Title

Mathematische Zeitschrift

Streaming Media

DOI

10.1007/s00209-022-03000-z