Generalized eigenfunctions of relativistic Schroedinger operators I

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Generalized eigenfunctions of the 3-dimensional relativistic Schrödinger operator √Δ + V(x) with |V(x)|≤ C < x >⁻σ, σ> 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 Schrödinger equation with the radiation condition. If σ>3, then we can give pointwise estimates of the differences between the sums and the solutions.