I'm trying to see what is the Fourier transform of the Skew normal distribution. My intuition and looking at some formulas for integrals about the error function suggests to me that it might be another Skew normal, just like the FT of a Gaussian is another Gaussian. I couldn't find any result on this question so I'm trying to derive it myself, but I want to know if this is a well know fact already.
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On the Wikipedia page you linked, the Characteristic Function (CF) is right there in the table on the top right hand side of the page. It indeed looks very much like a skew normal function. – Andy Walls Feb 16 '21 at 22:50