Many dynamical systems in fields such as neuroscience (the workings of the brain), systems biology (metabolic networks), and robotics (robot swarms) exhibit the structure of a network: they consist of nodes (neurons, proteins, robots) interconnected by edges. The specific architecture of these interactions can give rise to remarkably complex dynamics that go far beyond the behavior of individual nodes. Prominent examples include synchronization…
Abstract: The talk concerns density conditions for frames and Riesz sequences in the orbit of a square-integrable representation of a unimodular group. Among others, a simple proof for lattice orbits will be presented and various necessary conditions for general point sets will be discussed.
Bei Interesse an einer online-Teilnahme (sei es regelmäßig oder auch nur an einem bestimmten Vortrag) bitten wir vorab mit Tobias Weich Kontakt aufzunehmen,…
Abstract: In this talk we consider the centred and the uncentred Hardy--Littlewood maximal operators -- denoted $\cM$ and $\cN$, respectively -- on certain metric measure spaces with exponential volume growth and ``locally bounded geometry'' such as the hyperbolic upper half-plane and homogeneous trees.
A classical result of Hardy and Littlewood states that on the Euclidean space both $\cM$ and $\cN$ are bounded on $L^p$ for all $p>1$ and that…
