Generalized eigenfunctions of relativistic Schroedinger operators I

Details Generalized eigenfunctions of relativistic Schroedinger operators I Generalized eigenfunctions of relativistic Schroedinger operators I

2003-10-07

arxiv.org/abs/math/0310090v1

Mathematics

Spectral Theory

68 pages

Scientific paper

Generalized eigenfunctions of the 3-dimensional relativistic Schr\"odinger operator $\sqrt{\Delta} + V(x)$ with $|V(x)|\le C < x >^{{-\sigma}}$, $\sigma > 1$, 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.

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