 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-1/7d/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Using the convention adopted here, the Hilbert transform is

H f (y) = \frac{1}{π} PV \int_{- \infty}^{\infty} \frac{f ( x )}{y - x} d x .

The convention with denominator

x - y

differs by a minus sign.

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