The regularity of the transform of Laplace and the transform of Fourier

A. V. Pavlov

MIREA — Russian Technological University (Moscow)

Abstract: 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.

UDC: 517.53

Received: 27.11.2018
Accepted: 22.10.2020

DOI: 10.22405/2226-8383-2018-21-4-162-170