 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-1/4/a/solution

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

For example, the pointwise formula holds at continuity points under the usual integrability hypotheses; the same normalization applies to the

L^{2}

or distributional inverse.

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