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. 
@article{CHEB_2020_21_4_a15,
     author = {A. V. Pavlov},
     title = {The regularity of the transform of {Laplace} and the transform of {Fourier}},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {162--170},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_4_a15/}
}
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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/