Fourier Transform and Differential Equations

@inproceedings{Malgrange1991FourierTA,
  title={Fourier Transform and Differential Equations},
  author={B. Malgrange},
  year={1991}
}
We study, in the complex domain, the action of the Fourier transform on the solutions of ordinary linear differential equations with polynomial coefficients. In the classical “Laplace method”, there are some restrictions; also, some choice of integration contours seem rather unsystematic. We show how to remove these restrictions and how to make these choices in a more systematic way. 
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References

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