n This book deals with several aspects of fractal geometry in? which are closely connected
with Fourier analysis, function spaces, and appropriate (pseudo) differ-tial operators. It …

We establish an analogue of Weyl's classical theorem for the asymptotics of eigenvalues of
Laplacians on a finitely ramified (ie, pcf) self-similar fractal K, such as, for example, the …

A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem
is to describe the relationship between the shape (geo metry) of the drum and its sound (its …

Our main goal in this long survey article is to provide an overview of the theory of complex
fractal dimensions and of the associated geometric or fractal zeta functions, first in the case …

The present research monograph is a testimony to the fact that Fractal Analysis is deeply
connected to numerous areas of contemporary Mathematics. Here, we have in mind, in …

In this work, we study the steady-states vibrations of the “Koch snowflake drum”, both
numerically and by means of computer graphics. In particular, we approximate the smallest …

This note addresses two aspects of Minkowski measurability. First we present a short"
dynamical systems" proof of the characterization of Minkowski measurable compact subsets …

Let Ω be a non-empty open set in ℝn with finite 'volume'(n-dimensional Lebesgue measure).
Let be the Laplacian operator. Consider the eigenvalue problem (with Dirichlet boundary …

We construct spectral triples and, in particular, Dirac operators, for the algebra of continuous
functions on certain compact metric spaces. The triples are countable sums of triples where …

The Laplacian on a metric tree is on its edges, with the appropriate compatibility conditions
at the vertices. We study the eigenvalue problem on a rooted tree:-\lambda\Delta u= V …