Let $f$ be continuous, real valued and compactly supported with exactly one maximum function in $L_2$. Form the functions $ f_{m,k}=f^m(x-2^k) $
Under which conditions $\{f_{m,k}\}$ would be a frame?
(A function $f\in L_2(R)$ is said to generate a frame $\{f_{m,k}\}$ of $L_2(\mathbb{R})$ if for some $A$,$B>0$ we have $A\|f\|^2_2\le \sum_{j, k \in Z}|\langle f, f_{j,k}\rangle|^2\le B\|f\|^2_2$)
Thank you.