(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[itex](e_n)[/itex] is orthonormal basis for [itex]L^2([0,1])[/itex].

Want to show that [itex](f_n)[/itex] is basis for [itex]L^2([a,b])[/itex] when [itex]f_n(u) = (b-a)^{-1/2}e_n(\frac{u-a}{b-a})[/itex]

2. Relevant equations

[itex]f_n(u) = (b-a)^{-1/2}e_n(\frac{u-a}{b-a})[/itex]

3. The attempt at a solution

I did show that [itex] (f_n) [/itex] is an orthonormal sequence. But how can I show that it is also a basis...

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# Homework Help: Orthornormal basis in L^([a,b])

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