Question: Problem 10.9. Consider a casual function, g(t), such that g(t) = 0 for t 0. Let 81(2)= dte g(1) be the Laplace transform. Let F(w)=dt

Problem 10.9. Consider a casual function, g(t), such that g(t) = 0 for t 0. Let 81(2)= dte "g(1) be the Laplace transform. Let F(w)=dt eg(t) be the Fourier transform. Show that

8L (2) 00 8 'dw (BF (w)` 2 (BF (W)) = 8r

and show that the inverse transforms give the correct behavior for g(!).

8L (2) 00 8 'dw (BF (w)` 2 (BF (W)) = 8r (iz), iw)

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