it's a curiosity more than a HOmework, given the integral:(adsbygoogle = window.adsbygoogle || []).push({});

[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

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# A question on Fourier Analysis

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