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Are these fourier transforms?

  1. Mar 18, 2010 #1
    prove that f(x) = (1 + |x|)^{-a} is the fourier transform of some integrable function on R, when a > 1. what happens when 0 < a <= 1? how about the function f(x) = 1/(log(|x|^2 + 2))?
     
  2. jcsd
  3. Mar 18, 2010 #2

    jbunniii

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    Is this homework? If so, what have you done so far?
     
  4. Mar 18, 2010 #3
    yes, and i realize that we want the integral to converge when we take the inverse transform. so in order to do that, i'm guessing the denominator has to have a power > 1, which is why we have that condition on a. so it will fail the second time, i guess. but i can't formalize my argument (and i'm clueless about the third one).

    sry :(
     
  5. Mar 22, 2010 #4
    any help plz? :(
     
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