We show that solutions of the extension problem for the Laplacian $ \Delta $ on $ \R^n $ is closely connected to eigenfunctions of the Laplace-Beltrami operator on real hyperbolic spaces. When $ \Delta $ on $ \R^n $ is replaced by sublaplacians on certain two-step nilpotent Lie groups ( the so called Iwasawa N groups), the solutions of the associated extension problem are related to eigenfunctions of the Laplace-Beltrami operator on Riemmanian symmetric spaces of non-compact type. We address the problem of characterising the solutions of the extension problem when the nilpotent Lie group is a H-type group. This leads to an analogue of Helgason conjecture for Damek-Ricci spaces.


About Maths Colloquium

The Mathematics Colloquium is directed at students and academics working in the fields of pure and applied mathematics, and statistics. 

We aim to present expository lectures that appeal to our wide audience.

Information for speakers

Information for speakers

Maths colloquia are usually held on Mondays, from 2pm to 3pm, in various locations at St Lucia.

Presentations are 50 minutes, plus five minutes for questions and discussion.

Available facilities include:

  • computer 
  • data projector
  • chalkboard or whiteboard

To avoid technical difficulties on the day, please contact us in advance of your presentation to discuss your requirements.