 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-1/4/a/solution

For the stated forward Fourier transform, the inverse has the opposite exponential sign and a factor

1/ (2 π)

f (t) = \frac{1}{2 π} \int_{- \infty}^{\infty} f (ω) e^{iω t} d ω .

This holds under the usual hypotheses for Fourier inversion, or in the sense of distributions when appropriate.

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