POTENTIAL THEORY WITH MULTIVARIATE KERNELS
| Autor: | Dmitriy Bilyk, Damir Ferizović, Alexey Glazyrin, Ryan W. Matzke, Josiah Park, Oleksandr Vlasiuk |
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| Rok vydání: | 2022 |
| Předmět: | |
| Popis: | 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. Comment: 23 pages |
| Databáze: | OpenAIRE |
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