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Upper and lower bounds of a ratio involving vector norms
I'm working on a signal processing problem and need to analyze the following expression
$$
G = \frac{n}{\sum\limits_{i=1}^n |w_i|} \frac{ \sum\limits_{i=1}^n g_i w_i^2}{\sum\limits_{i=1}^n g_i |w_i|}
...
