Completeness of the generalized eigenfunctions for relativistic Schrödinger operators. I (Q2472328)

The scattering theory for the so-called relativistic Schrödinger operator \(\sqrt{-\Delta}+V\) for zero mass particles in presence of a short range potential perturbation \(V\) is considered in \(\mathbb{R}^{2k+1}\), \(k\in\mathbb{N}_{\geq1}\), in terms of generalized eigenfunction representations (perturbed Fourier transform). The limiting absorption principle for \(\sqrt{-\Delta}\) is utilized to construct bounded generalized eigenfunctions leading to generalized eigenfunction representations for the absolutely continuous part of the perturbed operator \(\sqrt{-\Delta}+V\). Completeness of the associated wave operators is obtained.