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Tricky Integral (fourier transforms)

  1. Nov 19, 2008 #1
    the question is on fourier transforms and i am stuck on how to approch the integral


    INT[ (1/(2*pi))*e^(ik(x-y)-(1+ik)ct) dk


    i know that the integral INT [(1/(2*pi))*e^(ik(x-y-ct)) dk] yields the delta function

    = DELTA(x-y-ct) but the terms in the exponential from the integral in question have stumped me

    any ideas would be great, cheers
     
  2. jcsd
  3. Nov 19, 2008 #2
    What don't you like about the delta function result?

    The e-ct is just a constant...
     
  4. Nov 19, 2008 #3
    would that mean we now have

    (INT[e^-ct]) *DELTA(x-y-ct) ?
     
  5. Nov 19, 2008 #4
    No, the integral is gone, but the constant still there. What you end up with is

    e-ctDelta(x-y-ct)
     
  6. Nov 19, 2008 #5
    cheers

    from that, the integral goes into the second integral

    u(x,t)=[INT (u(y, 0)dy*e^-ct*DELTA(x-y-ct))] - integrated over real space

    does this equal e^-ct*u(x-ct,0) ?
     
  7. Nov 19, 2008 #6
    Yes.
     
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