Riesz energy on self-similar sets
Alexander Reznikov; Oleksandr Vlasiuk · 2018 · arXiv
WASTE classifies this as Negative / Null Result Report · AI classification, approximate
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Abstract (excerpt)
We investigate properties of minimal $N$-point Riesz $s$-energy on fractal sets of non-integer dimension, as well as asymptotic behavior of $N$-point configurations that minimize this energy. For $s$ bigger than the dimension of the set $A$, we constructively prove a negative result concerning the asymptotic behavior (namely, its nonexistence) of the minimal $N$-point Riesz $s$-energy of $A$, but we show that the asymptotic exists over reasonable sub-sequences of $N$. Furthermore, we give a short proof of a result concerning asymptotic behavior of configurations that minimize the discrete Ries
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Metadata source: arXiv