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Fourier transform

  1. Apr 17, 2007 #1
    I am solving laplaces equation in the half plane and I have the following boundary condition of which I need to find the fourier transform in the x-direction

    [tex] S_\epsilon(x) = sgn(x)exp(\epsilon|x|), \epsilon >0 [/tex]

    [tex] sgn(x)=\left\{\begin{array}{cc}1,&\mbox{ if }
    x<0\\-1, & \mbox{ if } x<0\\ 0, &\mbox{ if } x=0\end{array}\right. [/tex]

    any hints on how to approach this FT??
     
    Last edited: Apr 17, 2007
  2. jcsd
  3. Apr 17, 2007 #2

    mjsd

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    Homework Helper

    there is a typo for the function sgn(x)? note that
    [tex]-S_\epsilon (x) = S_\epsilon (-x) [/tex] is an odd function... and you should get a Fourier sine series
     
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