Isotropic fractal drums

Abstract

Let Ω be a boundedC ^∞ domain in ${\mathbb{R}^n}$ where n∈ $\mathbb{N}$. Let Γ be a compact set in ${\mathbb{R}^n}$ with Γ ⊂ Ω. We described in 19.1 and in 19.2 what (in our context) is meant by a fractal drum where the influence of the membrane is characterized by a Radon measureμ with Γ = supp μ. An adequate mathematical description has been given 19.3 in terms of the operatorBin (19.25),

$$ B = {\left( { - \Delta } \right)^{ - 1}}^\circ t{r^\Gamma } $$

(23.1)

.