Let f be a differentiable complex valued function on R. If f is square integrable, then it is not the case that f(x) must approach zero at infinity. counterexample: f(x)=x^2 exp(-x^8 sin^2(20x)).(adsbygoogle = window.adsbygoogle || []).push({});

If I also require that the derivative of f be square integrable, is that enough to guarantee that lim x-> +/- infinity of f(x) is zero?

Thanks,

KH

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# Square integrable/vanish at infinity?

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