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 …

Based on his earlier work on the vibrations of 'drums with fractal boundary', the first author
has refined MV Berry's conjecture that extended from the 'smooth'to the 'fractal'case H …

We give an overview over the application of functional equations, namely the classical
Poincaré and renewal equations, to the study of the spectrum of Laplace operators on self …

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 …

Motivated in part by the first author's work [23] on the Weyl‐Berry conjecture for the
vibrations of 'fractal drums'(that is,'drums with fractal boundary'), ML Lapidus and C …

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 consider the asymptotic behaviour of the volume of the Minkowski sausage, the counting
function of the Dirichlet Laplacian, the partition function and the heat content for an iterated …

A formula for the interior is shown to match quite closely with earlier predictions of what it
should be, but is also much more precise. The resulting 'tube formula'is expressed in terms …