A convolution integral for Fourier transforms on the group \(\text{SL}(2, \mathbb C)\) (Q2528916)

The Fourier transform of a product of two functions on \(\text{SL}(2, \mathbb C)\) is expressed as a convolution integral of the Fourier transforms of its factors. With the help of this convolution integral we present the Fourier transform of a polynomially bounded function as a finite linear combination of analytic delta functionals applied to a continuous function on the real line in an improper sense.