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 …

The eigenvalues of the normalized Laplacian of a graph provide information on its
topological and structural characteristics and also on some relevant dynamical aspects …

We define sets with finitely ramified cell structure, which are generalizations of post-critically
finite self-similar sets introduced by Kigami and of fractafolds introduced by Strichartz. In …

Determining and analyzing the spectra of graphs is an important and exciting research topic
in mathematics science and theoretical computer science. The eigenvalues of the …

A thermodynamical treatment of a massless scalar field (a photon) confined to a fractal
spatial manifold leads to an equation of state relating pressure to internal energy, PV s …

In the quest for designing novel protocols for quantum information and quantum
computation, an important goal is to achieve perfect quantum state transfer for systems …

On fractals, spectral functions such as heat kernels and zeta functions exhibit novel features,
very different from their behaviour on regular smooth manifolds, and these can have …

In this paper we define (local) Dirac operators and magnetic Schrödinger Hamiltonians on
fractals and prove their (essential) self-adjointness. To do so we use the concept of 1-forms …

In this paper we study the spectral features, on fractal-like graphs, of Hamiltonians which
exhibit the special property of perfect quantum state transfer (PQST): the transmission of …

This paper provides explicit pointwise formulas for the heat kernel on compact metric
measure spaces that belong to a (N * N) N× N)-parameter family of fractals, which are …