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 …

Noncommutative Riemannian geometry and diffusion on ultrametric Cantor sets Page 1 J.
Noncommut. Geom. 3 (2009), 447–480 Journal of Noncommutative Geometry © European …

In this paper we define and study a gradient on pcf (post critically finite, or finitely ramified)
fractals. We use Dirichlet (energy) form analysis developed for such fractals by Kigami. We …

In a domain RN we consider compact, Birman–Schwinger type operators of the form TP; A
DA PA with P being a Borel measure in; containing a singular part, and A being an order N …

Let (A, H, D) be a spectral triple, namely: A is a C*-algebra, H is a Hilbert space on which A
acts and D is a selfadjoint operator with compact resolvent such that the set of elements of A …

We extend the noncommutative residue of M. Wodzicki on compactly supported classical
pseudo-differential operators of order− d and generalise A. Connes' trace theorem, which …