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

I am wondering if one can expand function $B(t)=1-|t|$, $t \in \mathbb{R}$ (this function called $B_1$ -spline) in terms of $f_{m,k}$, i.e. something like $1-|t|=\sum_{k,m}c_kf_{m,k} $

Thank you.

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do you mean local maximum or a global one? –  tomasz Jun 15 '12 at 23:58
    
also, do you mean composition or multiplication? –  tomasz Jun 16 '12 at 0:12
    
@tomasz: I ment global maximum.And its composition. –  David Jun 16 '12 at 0:41

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