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Square integrable/vanish at infinity?

  1. Aug 4, 2007 #1
    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)).
    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?

  2. jcsd
  3. Aug 4, 2007 #2


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    i think square integrable means the quare of the aBSOLUTE VAlue is finite.
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