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

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- Solution 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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