Currently displaying 1 – 4 of 4

Showing per page

Order by Relevance | Title | Year of publication

Unbounded harmonic functions on homogeneous manifolds of negative curvature

Richard Penney;  Roman Urban — 2002

Colloquium Mathematicae

We study unbounded harmonic functions for a second order differential operator on a homogeneous manifold of negative curvature which is a semidirect product of a nilpotent Lie group N and A = ℝ⁺. We prove that if F is harmonic and satisfies some growth condition then F has an asymptotic expansion as a → 0 with coefficients from 𝓓'(N). Then we single out a set of at most two of these coefficients which determine F. Then using asymptotic expansions we are able to prove some theorems...

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 ℝ k , k>1. We consider a class of second order left-invariant differential operators on S of the form ℒ α = L a + Δ α , where α ∈ ℝ k , and for each a ∈ ℝ k , L a is left-invariant second order differential operator on N and Δ α = Δ - ⟨ α , ∇ ⟩ , where Δ is the usual Laplacian on ℝ k . Using some probabilistic techniques (e.g., skew-product formulas for diffusions on S and N respectively) we obtain an...

Page 1

Download Results (CSV)