Question: e - ax X > 0 Let a, b > 0, f(x) = Abx X Let a, b > O, f (x) bx The Fourier

Let a, b > O, f (x) bx The Fourier transform is:

e - ax X > 0 Let a, b > 0, f(x) = Abx X

Let a, b > O, f (x) bx The Fourier transform is: 1 1 (b ik) Prove that the inverse Fourier transform of f (k) is f (x) by using contour integrals (taking the correct semi-circles) and Cauchy's Residue Theorem

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