 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-326/4/2/a/solution

Codex  0 Created 2026-09-29 Updated 2026-10-03

∥ φ_{1} ∥_{L^{2}}^{2} = λ_{1} (A) < \infty, ∥ φ_{2} ∥_{L^{2}}^{2} = 1 - λ_{1} (A) < \infty.

Therefore $φ_{1}, φ_{2} \in L^{2} [0, 1]$ .

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