Let L2[0, 1] be all bounded Riemann integrable functions [0, 1] → R with inner product (f, g) Split [0, 1] into intervals of length and on the k'th of them let Hnk be V2n on the first half of the interval, and -V2" on the second half. More precisely, So f(x)g(x) dx. Define functions Hnk as follows: V2", k+ < x < k 2n 2n Hn,k(x) = < x < k+1 2n 2", 2n 0, otherwise for n > 0, 0 < k < 2". Show that the Hn.k are orthonormal.
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Subtraction
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Q3. Math
![(3) Let L²[0, 1] be all bounded Riemann integrable functions [0, 1] → R with
inner product (f,g)
Split [0, 1] into intervals of length and on the k'th of them let Hn.k be
V2n on the first half of the interval,
precisely,
= Sr f(x)g(x) dx. Define functions H
n,k as follows:
2n
and -V2" on the second half. More
k+
< x <
k
2n.
2n
k+
1
Hn,k (x) =
2n,
2
2n
< x <
k+1
2n
0,
otherwise
for n > 0, 0 < k < 2". Show that the Hn.k are orthonormal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F675f8bcd-1ade-4607-a249-811066808762%2F20bcbb1d-0b1c-4e2b-b8d1-af1992d101b9%2F3x9iplv_processed.png&w=3840&q=75)
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