Riesz s-Equilibrium Measures on d-Dimensional Fractal Sets as s Approaches d

Details Riesz s-Equilibrium Measures on d-Dimensional Fractal Sets as s Approaches d Riesz s-Equilibrium Measures on d-Dimensional Fractal Sets as s Approaches d

2009-05-13

arxiv.org/abs/0905.2197v1

Mathematics

Classical Analysis and ODEs

Scientific paper

Let $A$ be a compact set in $\Rp$ of Hausdorff dimension $d$. For $s\in(0,d)$, the Riesz $s$-equilibrium measure $\mu^{s,A}$ is the unique Borel probability measure with support in $A$ that minimizes $$ \Is(\mu):=\iint\Rk{x}{y}{s}d\mu(y)d\mu(x)$$ over all such probability measures. In this paper we show that if $A$ is a strictly self-similar $d$-fractal, then $\mu^{s,A}$ converges in the weak-star topology to normalized $d$-dimensional Hausdorff measure restricted to $A$ as $s$ approaches $d$ from below.

Affiliated with

Also associated with

No associations

Rating

Riesz s-Equilibrium Measures on d-Dimensional Fractal Sets as s Approaches d does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Riesz s-Equilibrium Measures on d-Dimensional Fractal Sets as s Approaches d, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Riesz s-Equilibrium Measures on d-Dimensional Fractal Sets as s Approaches d will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-399526