If f(ω) is square integrable over the real ω-axis, then any one of the following implies the other two:
1. The Fourier transform F(t) = ℱ_ω[f(ω)](t) is 0 for t<0.
2. Replacing ω by z congruent x + i y, the function f(z) is analytic in the complex plane z for y>0 and approaches f(x) almost everywhere as y->0. Furthermore, integral_(-∞)^∞ ( left bracketing bar f(x + i y) right bracketing bar )^2 d x
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