7. Various applications. Extensions

7.1 Extending the Fourier transform to the complex field

One of the advantages of the Fourier transform is that it can often be extended to the complex field, i.e. the formula : $\hat{f} (z) = \int_{- \infty}^{\infty} e^{- 2 i π tz} f (t) d t$

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Various applications. Extensions

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References

(1) - DYM (H.), MC KEAN (H.P.) - Fourier Series and Integrals. - Academic Press 1972.
(2) - FOLLAND (G.) - Introduction to partial differential equations. - Princeton University Press 1976.
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