 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2017/ii/paper-2/24j/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-05

For

f \in L^{1} (R^{d})

, use the Fourier transform convention

f (ξ) = \int_{R^{d}} e^{- i ξ \cdot x} f (x) d x .

The integral is absolutely convergent for every

ξ

, and

∣ f (ξ) ∣ \leq ∥ f ∥_{1}

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