### Author Topic: Problem 1--simplified  (Read 20642 times)

#### Victor Ivrii

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##### Re: Problem 1--simplified
« Reply #15 on: November 07, 2012, 09:46:05 PM »

Everybody: I did not ask you to take all integrals. Instead after you found F.T. of $e^{-\alpha |x|}$ (say $G(\omega)$) you recalling properties of F.T understand that F.t. of $e^{-\alpha |x|}e^{\pm i\beta x}$ are  $G(\omega \mp \beta)$ and then F.T. of  $e^{-\alpha |x|}\cos(\beta x)$ and $e^{-\alpha |x|}\sin(\beta x)$ are $\frac{1}{2}[ G(\omega - \beta)+G(\omega + \beta)]$ and $\frac{1}{2i}[ G(\omega - \beta)-G(\omega + \beta)]$ respectively