The bounded spherical functions for the free two step nilpotent Lie group

Abstract

In this paper, we give the expressions for the bounded spherical functions, or equivalently the spherical functions of positive type, for the free two-step nilpotent Lie groups endowed with the actions of orthogonal groups or their special subgroups. Next we deduce some results about the (Kohn) sub-Laplacian, and we compute the radial Plancherel measure.

arXiv commentPublished in 2006

Cited by in corpus (2)

• The spherical transform of a Schwartz function on the free two step nilpotent lie group
• Spectra for Gelfand pairs associated with the free two step nilpotent lie group