2021/11/18 by Fischer, Veronique
#35K08 #35P05 #43A85 #53C17 #58J35 #58J50 #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2112.01246
In this paper, we obtain asymptotic formulae on nilmanifolds Γ\backslash G, wher 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.