2

I got the following question at my homework:The question

I got stuck in (2). I saw proof for that is orthonormal, but I don't know how to proof close system. I don't know even for which function those Walsh function are basis of, does it a basis of all constants? if yes why? if it is, can I use the same method of proving Haar system is close or not?

the proof of orthonormal: enter image description here

Mr.O
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  • 2 questions: what is a "closed orthonormal system" anyway? (According to your book.) And what is $L_{\mbox{pc}}^2[0,1]$? – kimchi lover Nov 25 '17 at 23:55

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