Lie Symmetries of Fundamental Solutions to the Leutwiler-Weinstein Equation.

In this article, we study Lie symmetries to fundamental solutions to the Leutwiler-Weinstein equation L u : = Δ u + k x n ∂ u ∂ x n + ℓ (x n) 2 u = 0 in the upper half-space ℝ + n . Starting from the infinitesimal generators of the equation Lu = 0, we deduce symmetries of the equation Lu = δ(x − x₀), and using its invariant solutions, we construct a fundamental solution. As an application, we study a Green functions of the operator in the hyperbolic unit ball. [ABSTRACT FROM AUTHOR]