The <indicator function>[indicator functions] satisfy
$$
\|\varphi_1\|_{L^2}^2=\lambda_1(A)<\infty,
\qquad
\|\varphi_2\|_{L^2}^2=1-\lambda_1(A)<\infty.
$$
Therefore $\varphi_1,\varphi_2\in L^2[0,1]$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 326 / 4 / 2 / a / Solution

 Solution

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