Abstract:The usual solution to the Dirichlet problem for the Laplace equation Δu = 0 in the slab R n × (a, b), where −∞ < a < b < ∞, and the half-space R n ×(0, ∞) involves convolution of the data with a Poisson kernel. Interestingly, the class of distributions which is convolvable with the natural Poisson kernel Q for the slab is considerably wider than that which is convolvable with the classical Poisson kernel P for the half-space. We investigate this curious phenomenon and observe that arbitrary tempered distributi… Show more
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