Centered densities on Lie groups of polynomial volume growth (Q1849737)

The article studies the asymptotic behavior of the convolution powers of a centered density \(\varphi\) on a connected Lie group G of polynomial volume growth. The main tool is a Harnack inequality. It is shown that the positive \(\varphi\)-harmonic functions are constant. There is also given a characterization of the \(\varphi\)-harmonic functions which grow polynomially, and Gaussian estimates for convolution powers.