4. Let H = {Hmm NU {0}} be the sequence of Haar functions. Consider the...

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4. Let H = {Hmm € NU {0}} be the sequence of Haar functions. Consider the inner product space (L²(R), (...)) where and for any f, g € L² (R), = {√₁R+R √ 1² <∞}, L²(R) = (f,g) = [ fg. (a) (Unit) Prove that [Hm(t)]² dt = 1 for any m € NU {0}. R (Hence Hm E L2(R) and ||Hm|| 1.) = 4. Let H = {Hmm € NU {0}} be the sequence of Haar functions. Consider the inner product space (L²(R), (...)) where and for any f, g € L² (R), = {√₁R+R √ 1² <∞}, L²(R) = (f,g) = [ fg. (a) (Unit) Prove that [Hm(t)]² dt = 1 for any m € NU {0}. R (Hence Hm E L2(R) and ||Hm|| 1.) =