Geodesic
The regularity of the transform of Laplace and the transform of Fourier
Čebyševskij sbornik, Tome 21 (2020) no. 4, pp. 162-170.

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The paper proves the regularity in a neighborhood of zero of the Laplace transform of the Fourier transform of an even function obtained from an odd function regular in a neighborhood of the real axis by changing the parity. This fact implies that the sine and cosine of the Fourier transforms are commutable up to the sign.
Keywords: Fourier transform, sine and cosine Fourier transform transposition, Laplace transform regularity of Fourier transform. 
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A. V. Pavlov. The regularity of the transform of Laplace and the transform of Fourier. Čebyševskij sbornik, Tome 21 (2020) no. 4, pp. 162-170. http://geodesic.mathdoc.fr/item/CHEB_2020_21_4_a15/

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