A question on Fourier Analysis

1. Apr 25, 2007

tpm

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

$$\int_{-\infty}^{\infty}dx e^{if(x)+iwx}=g(w)$$

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:

$$-if'(x)\frac{\partial g(w)}{\partial w}+wg(w)=0$$

for simplicity we can impose $$exp(if(\infty))=0$$ and the same for

-oo

2. Apr 25, 2007

AiRAVATA

Why don't you derive and show us if it's true?

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