In this paper a generalization of a classic result of H. Weyl concerning the asymptotics of the spectrum of the Laplace operator is proved for variational fractals. Physically we are studying the density of states for the diffusion trough a fractal media. A variational fractal is a couple where is a self-similar fractal and is an energy form with some similarity properties connected with those of . In this class we can find some of the most widely studied families of fractals as nested fractals, p.c.f. fractals, the Sierpinski carpet etc., as well as some regular self-similar Euclidean domains. We will see that if is the number of eigenvalues associated with smaller than , then , where is the intrinsic dimension of .
Cite this article
G. Posta, Spectral Asymptotics for Variational Fractals. Z. Anal. Anwend. 17 (1998), no. 2, pp. 417–430DOI 10.4171/ZAA/830