On some integral operators appearing in scattering theory, and their resolutions

We discuss a few integral operators and provide expressions for them in terms of smooth functions of some natural self-adjoint operators. These operators appear in the context of scattering theory, but are independent of any perturbation theory. The Hilbert transform, the Hankel transform, and the finite interval Hilbert transform are among the operators considered.
Comment: 13 pages, to appear in the Proceedings of STMP 2018