# Algorithm for Gram-Schmidt orthogonalization process

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 $\{f_{m,k}(x)\}$?

- 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