One criterion of unitarity of bilateral integral transformation - Vu Kim Tuan; Yakubovich , S. B. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
A criterion for a two-sided Watson transform to be unitary in the space L2 (R) is considered. It enables us to construct new examples of integral transforms with symmetric inversion formulas (only the Fourier and the Hartley transforms are known). We give some new examples of the indicated transforms, in particular, the symmetric Hankel transform with the sum of two Bessel functions in the kernal and the Hardy transform with the sum of a Neumann function and a Struve function in the kernel, and the Narain transform with a sum of two G-functions in the kernel.