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…