Talks

Prony's problem - estimating the frequencies of an exponential sum - and its higher dimensional
analogs have attracted a lot of attention in recent years. A somewhat neglected question is whether
this problem is well-posed. In this talk, some results in this direction will be presented.
We start by giving a brief introduction to stability in compressed sensing. Compressed sensing is
concerned with solving nite dimensional linear systems under a priori sparsity assumptions. Stability
follows from the so-called restricted isometric property (RIP) of the system matrix.
We then discuss sparse frequency estimation. Due to the continuous nature, proving an analogue of
the RIP is more dicult. To this end, we briey introduce specic functions, which are well localized
in the spatial and frequency domain. Then we deduce stability results as well as a posteriori error
estimates.
This talk is based on joint work with Armin Iske.

In [Doc. Math. 4 (1999),275--283], Griesemer, Lewis, and Siedentop devised an abstract minimax principle for eigenvalues in spectral gaps of perturbed self-adjoint operators. We show that this minimax principle can be adapted to the particular situation of bounded additive perturbations with hypotheses that are easier to check in this case. The latter is demonstrated in the framework of the Davis-Kahan sin(2\Theta) theorem.

This talked is based on joint work with I. Nakic, M. Täufer, M. Tautenhahn, and I. Veselic.

I'll start with a short recap of the lattice Anderson
model, with a focus on Minami's estimate and its applications. In
particular it implies Poissonian local eigenvalue statistics, which
is believed to be a characteristic feature of spectrally localized
quantum mechanical systems. In the second part of the talk I'll
present our main technical result, a level-spacing estimate for
continuum random Schrödinger operators, and argue why it implies
Poissonian local eigenvalue statistics. If time permits I'll comment
on the proof's methods.
The talk is based on joint work with Alexander Elgart.

We are going to discuss (again) the approach of describing fractional powers of linear operators on
Banach spaces as it was performed by Silvestre and Caffarelli when they were studying the fractional
Laplacian. Even though useful it is still an open problem whether this is possible for all sectorial
operators and, if so, whether it is unique.
The presented content is work in progress.