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A question on Fourier Analysis

  1. Apr 25, 2007 #1

    tpm

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    it's a curiosity more than a HOmework, given the integral:

    [tex] \int_{-\infty}^{\infty}dx e^{if(x)+iwx}=g(w) [/tex]

    Where g(w) can be viewed as the Fourier transform of exp(if(x)) then my question is if we can prove g(w) satisfies the ODE:

    [tex] -if'(x)\frac{\partial g(w)}{\partial w}+wg(w)=0 [/tex]

    for simplicity we can impose [tex] exp(if(\infty))=0 [/tex] and the same for

    -oo
     
  2. jcsd
  3. Apr 25, 2007 #2
    Why don't you derive and show us if it's true?
     
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