Laplace Operators on Fractals and Related Functional Equations

We give an overview over the application of functional equations, namely the classical Poincar\'e and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals. We compare the techniques used to those used in the euclidean situation. Furthermore, we use the obtained information on the spectral zeta function to define the Casimir energy of fractals. We give numerical values for this energy for the Sierpi\'nski gasket

Spectral Properties of Random Schrödinger Operators with Unbounded Potentials

We investigate spectral properties of random Schrödinger operators H_ω = - Δ + ξ_n(ω)(1 + │n│^ɑ) acting on l^2(Z^d), where ξ_n, are independent random variables uniformly distributed on [0, 1]

Spectral Properties of Random Schrödinger Operators with Unbounded Potentials

We investigate spectral properties of random Schrödinger operators H_ω = - Δ + ξ_n(ω)(1 + │n│^ɑ) acting on l^2(Z^d), where ξ_n, are independent random variables uniformly distributed on [0, 1]