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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.
Original language | English |
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Pages (from-to) | 2907-2935 |
Number of pages | 23 |
Journal | Mathematische Zeitschrift |
Volume | 301 |
DOIs | |
Publication status | Published - 2022 |
Keywords
- Classical Analysis
- Functional Analysis
ASJC Scopus subject areas
- Analysis
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Potential Theory with Multivariate Kernels I
Damir Ferizović (Speaker)
27 Jan 2021Activity: Talk or presentation › Talk at workshop, seminar or course › Science to science