 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-1/4/i/solution

With the stated negative sign in the forward exponential, the inverse Fourier transform is

f (x) = \frac{1}{2 π} \int_{- \infty}^{\infty} f (k) e^{ik x} d k .

For example, this holds pointwise for Schwartz functions; more general square-integrable functions use the corresponding mean-square interpretation.

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