Riesz s-Equilibrium Measures on d-Dimensional Fractal Sets as s Approaches d
| dc.creator | Calef, Matthew T. | |
| dc.date | 2009-05-13 | |
| dc.date.accessioned | 2026-07-07T13:14:53Z | |
| dc.date.available | 2026-07-07T13:14:53Z | |
| dc.description | Let $A$ be a compact set in $\Rp$ of Hausdorff dimension $d$. For $s\in(0,d)$, the Riesz $s$-equilibrium measure $μ^{s,A}$ is the unique Borel probability measure with support in $A$ that minimizes $$ \Is(μ):=\iint\Rk{x}{y}{s}dμ(y)dμ(x)$$ over all such probability measures. In this paper we show that if $A$ is a strictly self-similar $d$-fractal, then $μ^{s,A}$ converges in the weak-star topology to normalized $d$-dimensional Hausdorff measure restricted to $A$ as $s$ approaches $d$ from below. | |
| dc.identifier | https://arxiv.org/abs/0905.2197 | |
| dc.identifier | http://arxiv.org/abs/0905.2197 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230322 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 31C15 | |
| dc.title | Riesz s-Equilibrium Measures on d-Dimensional Fractal Sets as s Approaches d | |
| dc.type | text |