Q3. Please explain clearly, please solve correctly. Math real Analysis

(3) Let L2[0, 1] be all bounded Riemann integrable functions (0, 1] - R with inner product (f, g) = Jo f(x)g(x) dx. Define functions Hn.k as follows: Split [0, 1] into intervals of length mm and on the k'th of them let Hn,k be V2" on the first half of the interval, and -V2" on the second half. More precisely, kt : V 2n k 2n 2n Hn, k (x) = V2n ktz 2n 2n otherwise for n 2 0, 0