In his answer to Bitrex's question, Sasha used generalized function properties to derive the Fourier transform of order $0$ Bessel function of the first kind.
I can't work out the logic he used in his answer.
Can someone please clarify this for me?
Maybe mention the identities used in the derivation of the answer?
I'm Mainly puzzled by the transition to the third row, and the notation in the following, fourth row: −1≤ω≤1 .