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The evolution and Poisson kernels on nilpotent meta-abelian groups

Richard Penney, Roman Urban (2013)

Studia Mathematica

Let S be a semidirect product S = N⋊ A where N is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and A is isomorphic to k , k>1. We consider a class of second order left-invariant differential operators on S of the form α = L a + Δ α , where α k , and for each a k , L a is left-invariant second order differential operator on N and Δ α = Δ - α , , where Δ is the usual Laplacian on k . Using some probabilistic techniques (e.g., skew-product formulas for diffusions on S and N respectively) we obtain an...

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