07-3   Berichtsreihe des Mathematischen Seminars der Universität Kiel

## A.e. convergence of spectral sums on Lie groups

Let $\L$ be a right-invariant sub-Laplacian on a connected Lie group $G,$ and let $S_Rf:=3D \int_0^R dE_\la f,\ R\ge 0,$ denote the associated spherical partial sums,'' where $\L=3D\int_0^\infty \la\, dE_\la$ is the spectral resolution of $\L.$ We prove that $S_Rf(x)$ converges a.e. to $f(x)$ as $R\to\infty$ under the assumption \$\log(2+\L)f\in L^2(G)

Mathematics Subject Classification (1991): 22E30 and 43A50

Bibliographical note: to appear Ann. Inst. Fourier.

Keywords: Rademacher-Menshov theorem, sub-Laplacian, spectral theory