Generalized Fourier transforms classes

The Fourier class of integral transforms with kernels B(ωr) has by definition inverse transforms with kernel B(-ωr). The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory follows that integral transform with kernels which are products of a Bessel and a Hankel function or which is of a certain general hypergeometric type have inverse transforms of the same structure.