# not $L^2$ function and appropriate weight

I've learned that I can carry a non $L^{2}$ function with an appropriate weight function in to $L^{2}$ space. But I can't find any example on it.(probably, just because it is very simple:(). Let $f(x)=1/x$, so f is not in $L^{2}(\mathbb{R})$ but I should find a function $g(x)=w(x)f(x)$ which is in $L^2$. Is it possible to find such an exponential function?

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## migrated from stackoverflow.comAug 24 '12 at 13:43

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Why has it to be an expontential function? How about w(x) = x? – flolo Aug 23 '12 at 9:16
Belongs on math. – Klas Lindbäck Aug 23 '12 at 11:44
This question has a really stupid answer: take $w\equiv 0$. You should tell us what conditions $w$ must satisfy. But, in general, there are infinitely many non-trivial functions that solve your problem. – Siminore Aug 24 '12 at 13:49