In this paper, we obtain asymptotic formulae on nilmanifolds Γ﹨G, where G is any stratified (or even graded) nilpotent Lie group equipped with a co-compact discrete subgroup Γ. We study especially the asymptotics related to the sub-Laplacians naturally coming from the stratified structure of the group G (and more generally any positive Rockland operators when G is graded). We show that the short-time asymptotic on the diagonal of the kernels of spectral multipliers contains only a single non-trivial term. We also study the associated zeta functions.
- Global analysis and spectral problems
- Harmonic analysis on homogeneous spaces
- Heat kernels
- Hypoelliptic operators
- Spectral multipliers
ASJC Scopus subject areas
- Applied Mathematics