 Solution

ID: past-exam-of-the-algebra-1-and-differential-equations-1-course-of-the-university-of-oxford/2014/6/a/solution

v (ω) = \int_{- \infty}^{\infty} v (x) e^{- iω x} d x .

v

makes this integral exist for every real

ω

, with

∣ v (ω) ∣ \leq ∥ v ∥_{1}

. With this convention the inverse Fourier transform has factor

1/ (2 π)

; maintaining that normalization is essential in part (e).

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