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Fourrier Tranform and schwartz space

  1. Jan 30, 2012 #1
    ^_f=fourrier transform of f.
    f_k=f<sub>k
    sqrt= square root

    The function f belongs to the schwartz space and k>0 f_k(x)=f(kx).
    1)show that f_k also belongs to the schwartz space and ^_f(e)=(1/k)^_f(e/k)
    2)the fourrier transform of exp((−x^2)/2) is sqrt(2pi)*exp((−e^2)/2) use the first part to obtain the fourrier transform for exp(−ax^2)

    Attempt:
    f belongs to the schwartz space then f is infinitly diff also f(kx)=kf(x) which belongs to the schwartz space.
    then f_k(x)=f(kx)=kf(x) which belongs to the schwartz space.
    I don't know if this is correct or how to continue...any help will be great.Thank you
     
  2. jcsd
  3. Jan 30, 2012 #2
    Should I change something ?
     
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