Fractional kinetic equations of the diffusion, diffusion–advection, and Fokker–Planck type
are presented as a useful approach for the description of transport dynamics in complex …

Wavelet techniques in multifractal analysis Page 1 2585-30 Joint ICTP-TWAS School on
Coherent State Transforms, TimeFrequency and Time-Scale Analysis, Applications S. Jaffard 2 …

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 …

Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study
of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. Key …

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 …

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 theory of fractal strings and their complex dimensions investigates the geometric,
spectral and physical properties of fractals and precisely describes the oscillations in the …

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 …