Generalized eigenfunctions of relativistic Schroedinger operators I

Generalized eigenfunctions of the 3-dimensional relativistic Schr"odinger operator $\sqrt{\mathrm{\Delta }}+V(x)$ with $\mathrm{\mid }V(x)\mathrm{\mid }\le C<x{>}^{-\sigma }$, $\sigma > 1$, are considered. We show that the generalized eigenfunctions can be expressed as the sum of plane waves and solutions to the time-independent relativistic Schr"odinger equation with the radiation condition. If $\sigma

3$, then we can give pointwise estimates of the differences between the sums and the solutions.