 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-1/4/e/solution

α = 1

in part (d), obtaining

F [e^{- ∣ t ∣}] (ω) = 2/ (1 + ω^{2})

2 F [\frac{1}{1 + t ^{2}}] (ω) = 2 π e^{- ∣ ω ∣} .

Therefore

s (ω) = π e^{- ∣ ω ∣} .

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