Thursday, January 26, 2023
01/26/2023 - 4:00pm
A subgroup H of a countable group G is co-amenable if the left regular representation on the coset space G/H admits almost invariant vectors. Co-amenablility is a notion of largeness of a subgroup, but it is not the best behaved one. For example, the intersections of co-amenable subgroups can fail to be co-amenable. I will talk about a joint work with Wouter van Limbeek in which we prove that the class of co-amenable invariant random subgroups is closed under taking finite intersection. This follows from more general results on the co-spectral radii of intersections of invariant random subgroups.
01/26/2023 - 4:15pm
We describe recent remarkable nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It is known that all harmonic functions in higher dimensions are combinations of holomorphic functions on 2 dimensional planes, extended as, constant in normal directions. We derive representation theorems, with corresponding isometries, opening the door for applications in higher dimensions, to the processing of highly oscillatory multidimensional signals.
This is joint work with Guido Weiss Stefan Steinerberger , Jacques Peyriere , Hau -tieng Wu and many others