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Nowhere stationary phase

  1. Sep 20, 2011 #1
    Hi all,
    I have an integral defined as a fourier transform of the exponential of a function:
    [tex] \mathcal{A}(\mathbf{q})=\int d^2 b e^{i \mathbf{q} \cdot \mathbf{b}}(e^{i \chi(\mathbf{b})}-1)[/tex]
    Approximating this integral via the stationary phase method (neglecting here the question of a small parameter), we look for points where
    [tex]\frac{d\chi}{db}=q[/tex]
    However, it turns out that the derivative of my function chi is bounded above, and I'm interested in values of q that exceed my maximum value of d(chi)/db. Is there anything I can say about this integral if I can't calculate it?
     
  2. jcsd
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