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

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Past exam of the mathematics course of the University of Cambridge / 2017 / ii / Paper 2 / 24J / b / Solution by

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

Here Fourier inversion means the absolute-integral version:

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

and

f (x) = (2 π)^{- d} \int_{R^{d}} e^{i ξ \cdot x} f (ξ) d ξ for almost every x .

(1)

This convention is necessary for the bounded continuous version in part (d). Conditional inversion by symmetric truncation is a different statement and need not have that conclusion.

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