Fundamental solution

Hi,

Hörmander: The analysis of partial differential operators, Vol.I, Chapter 6.2, proves that a fundamental solution E of the wave equation, i.e. P(D)E(t,x) = delta(t,x), also solves the Cauchy problem:

P(D)u = 0, u(0,x) = g(x), u'(0,x) = delta(x)

I am struggling with an argument on page 141 where E+, the part of E supported on the future light cone, is written as an integral

<E+, phi> = integral(0 to infinity) <E+(t), phi(t,.)> dt

He writes that "E+ is a fundamental solution of the wave equation, therefore E+(0) = 0, E'+(0) = delta(x)"

So we have <P(D)E+, phi)> = phi(0,0), but what does this mean for E+(0) ?

Andy
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