L. Hörmander's extension of Ásgeirsson's mean value theorem states that if
u is a solution of the inhomogeneous ultrahyperbolic equation
(Δx−Δy)u=f,
x,yRν,
fE′(R2ν), then
Formula Not Shown where
t is positive and
μt is given explicitly. Whereas L. Hörmander proves this by defining
μt without much motivation and then verifying the equation
Formula Not Shown the aim of this article is a
constructive deduction of a slightly different representation of the distribution
μt, viz.
μt is the analytic continuation of
Formula Not Shown into the value
z=ν, where
A=t4−2t2(x2+y2)+(x2−y2)2.