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Let $f$ be a continuous function on $\mathbb{R}$ with compact support with exactly one maximum. Form the functions $$ f_{m,k}(x)=f^m\left(x-\frac{k}{2^m}\right), k \in Z, m>0. $$

Fix $m$. How one would do the Gram-Schmidt orthogonalization process for $\{f_{m,k}(x)\}$?

Thank you for your help.

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The same as always? What's stumping you up? Are you looking for a nice formula? –  tomasz Jun 19 '12 at 20:20
    
Yes, I would like to get a nice representation. –  David Jun 19 '12 at 21:18
    
- I guess $n$ should be $m$. - What do you mean by $f^m$? Is it the $m-th$ power of $f$ or the $m-th$ iterate? –  bartgol Jun 20 '12 at 14:48
    
Thank you.It is $m$-th power. –  David Jun 21 '12 at 2:44
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