Localisation of Spectral Sums Corresponding to the Sub-Laplacian on the Heisenberg Group

In this article we study localisation of spectral sums {S-R}(R>0) associated with the sub-Laplacian L on the Heisen-berg Group H-d where S(R)f := integral(R)(0) dE(lambda)f, with L = integral(infinity)(0) lambda dE(lambda) being the spectral resolution of L. We prove that for any compactly supported function f is an element of L-2(H-d), and for any gamma <1/2, R(gamma)S(R)f -> 0 as R -> infinity, almost everywhere off supp(f ).