Abstract:Classical Fourier analysis on $\mathbb{R}^n$ yields fundamental inequalities such as Pitt’s inequality and the Heisenberg-type uncertainty principle. In this talk, we describe recent progress in extending these results to Riemannian symmetric spaces of noncompact type. In particular, we establish an analogue of Pitt’s inequality for the Helgason Fourier transform and for the Jacobi transform. We also discuss the corresponding uncertainty inequalities, highlighting how the non-Euclidean geometry of these spaces leads to new admissibility conditions and weight regimes that do not appear in the Euclidean setting.
Bei Interesse an einer online-Teilnahme (sei es regelmäßig oder auch nur an einem bestimmten Vortrag) bitten wir vorab mit Tobias Weich Kontakt aufzunehmen, damit der Teilnahmelink geteilt werden kann.