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  • $\begingroup$ @yarchik: Can you ground your claim giving us an accessible reference? TIA. $\endgroup$ Commented Feb 23, 2022 at 12:05
  • $\begingroup$ @yarchik: Wiki says "The Fourier transform translates between convolution and multiplication of functions. If f(x) and g(x) are integrable functions with Fourier transforms f̂(ξ) and ĝ(ξ) respectively, then the Fourier transform of the convolution is given by the product of the Fourier transforms f̂(ξ) and ĝ(ξ) (under other conventions for the definition of the Fourier transform a constant factor may appear).". $\endgroup$ Commented Feb 23, 2022 at 12:13
  • $\begingroup$ @yarchik: Sorry, don't understand you. Ungrounded statements do not make a good impression. Can you elaborate your previous comment, giving us a possible answer to the question? TIA. $\endgroup$ Commented Feb 23, 2022 at 12:47
  • $\begingroup$ @yarchik: Sorry, again ungrounded $$\int dx f(x) g(x) = \int dt \mathcal{F}[f](t) \mathcal{F}[g](-t).$$ It should be noticed that InverseFourierTransform[Convolve[Exp[-Abs[t]], I/t, t, y], y, t] returns the input. $\endgroup$ Commented Feb 23, 2022 at 12:51
  • $\begingroup$ @yarchik: If I state a non-trivial claim, I try to give an accessible reference to it. $\endgroup$ Commented Feb 23, 2022 at 15:20