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Fourier representation of aperiodic irregular function

  1. Mar 2, 2007 #1
    We have

    [tex]\epsilon(i f, r) = \epsilon_2(i f)[/tex] when [tex]H + h_2(x) \leq z < + \infty[/tex]
    [tex]\epsilon(i f, r) = 0[/tex] when [tex]h_1(x) < z < H + h_2(x)[/tex]
    [tex]\epsilon(i f, r) = \epsilon_1(i f)[/tex] when [tex]- \infty < z \leq h_1(x)[/tex]

    show the corresponding Fourier transform is

    [tex]\frac{i}{q_z} \int d^2x e^{iq_\bot \cdot x}[\epsilon_2 e^{iq_z[H+h_2(x)]} - \epsilon_1 e^{iq_z h_1(x)}][/tex]

    I've looked in a few books but tbh I have no real idea how to show this...

    Any help/suggestions/tips would be much appreciated. Thanks.
    Last edited: Mar 2, 2007
  2. jcsd
  3. Mar 4, 2007 #2
    a small hint please?
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