ABSTRACT
We are now interested in finding the analog of the Poisson kernel for the Dirichlet problem for the perturbed Laplacian on the upper half space {(x, t) : x ∈ Rn, t > 0} given by
{ ∂2u ∂t2 (x, t) + ((∆−m2)u)x, t) = 0, x ∈ Rn, t > 0, u(x, 0) = f(x), x ∈ Rn, (12.1)
where m is a positive constant and f is a function in S. It turns out that the resulting kernel Wt(x), x ∈ Rn, t > 0, is the product of the Poisson kernel and a weighted Bessel potential.
