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How to perform Fourier transform of a multivalued function?

  1. May 22, 2015 #1

    There is the following function whose Fourier transform I cannot work out despite days of labour,
    $$f(q) = \frac{e^{i\sqrt{q^2+1}a}}{\sqrt{1+q^2}}.$$ Here ##a## is a nonnegative constant. As usual, the Fourier transform is
    $$F(x) = \int^{\infty}_{-\infty}dq~e^{iqx}f(q).$$ I tried to use contour integral, but the integrand has branch points in the complex plane. I could not find a proper contour which can make a de tour off the branch cuts!

    Could you give me some advice?

    Thank you !

  2. jcsd
  3. May 27, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
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