  Generalized eigenfunctions of the two-dimensional relativistic Schr\"odinger
operator $H=\sqrt{-\Delta}+V(x)$ with $|V(x)|\leq C< x>^{-\sigma}$,
$\sigma>3/2$, are considered. We compute the integral kernels of the boundary
values $R_0^\pm(\lambda)=(\sqrt{-\Delta}-(\lambda\pm i0))^{-1}$, and prove that
the generalized eigenfunctions $\phi^\pm(x,k)$ are bounded on $R_x^2\times\{k |
a\leq |k|\leq b\}$, where $[a,b]\subset(0,\infty)\backslash\sigma_p(H)$, and
$\sigma_p(H)$ is the set of eigenvalues of $H$. With this fact and the
completeness of the wave operators, we establish the eigenfunction expansion
for the absolutely continuous subspace for $H$. Finally, we show that each
generalized eigenfunction is asymptotically equal to a sum of a plane wave and
a spherical wave under the assumption that $\sigma>2$.
