The Journal of Geometric Analysis

, Volume 2, Issue 3, pp 213–248

Harmonic analysis on solvable extensions of H-type groups


  • Ewa Damek
    • Instytut Matematyczny Universytetu Wroclawskiego
  • Fulvio Ricci
    • Dipartimento di MatematicaPolitecnico di Torino

DOI: 10.1007/BF02921294

Cite this article as:
Damek, E. & Ricci, F. J Geom Anal (1992) 2: 213. doi:10.1007/BF02921294


To each groupN of Heisenberg type one can associate a generalized Siegel domain, which for specialN is a symmetric space. This domain can be viewed as a solvable extensionS =NA ofN endowed with a natural left-invariant Riemannian metric. We prove that the functions onS that depend only on the distance from the identity form a commutative convolution algebra. This makesS an example of a harmonic manifold, not necessarily symmetric. In order to study this convolution algebra, we introduce the notion of “averaging projector” and of the corresponding spherical functions in a more general context. We finally determine the spherical functions for the groupsS and their Martin boundary.

Math Subject Classification


Key Words and Phrases

Harmonic manifoldsHeisenberg type groupsMartin boundarysolvable Lie groupsspherical functions

Copyright information

© CRC Press, Inc 1992