Aarhus University Seal / Aarhus Universitets segl

On some boundary value problems on nilpotent groups (joint w/ Bent Ørsted, Genkai Zhang)

Jan Möllers
Torsdag, 15 maj, 2014, at 16:15, in Aud. D3 (1531-215)
We interpret certain boundary value problems on some nilpotent groups as restriction problems for representations of semisimple Lie groups. Recently developed techniques in representation theory then allow us to find the corresponding Poisson transforms as explicit integral operators and to show that they are isometries between certain Sobolev type spaces of boundary values and solutions.

This extends recent results by Caffarelli-Silvestre for the nilpotent group $\mathbb{R}^n$, and by Frank et al. for the Heisenberg group $\mathbb{C}^n+\mathbb{R}$.
Kontaktperson: Bent Ørsted