Abstract
Let S be a Damek–Ricci space and Δ be the Laplace–Beltrami operator of S. We explore the behaviour of heat propagator in S in large time to illustrate the differences with the corresponding results in Rn. In particular we study the relation between the limiting behaviour of the ball-averages as radius tends to ∞ and that of the heat propagator as time goes to ∞ and use this relation for characterization of eigenfunctions of Δ.
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