Generalized eigenfunctions of the 3-dimensional relativistic Schrodinger operator with , , are considered. We construct the generalized eigenfunctions by exploiting results on the limiting absorption principle. We compute explicitly the integral kernel of , , which has nothing in common with the integral kernel of , but the leading term of the integral kernels of the boundary values , , turn out to be the same, up to a constant, as the integral kernels of the boundary values . This fact enables us to show that the asymptotic behavior, as , of the generalized eigenfunction of is equal to the sum of a plane wave and a spherical wave when .
Submitted September 22, 2006. Published October 11, 2006.
Math Subject Classifications: 35P99, 35S99, 47G30, 47A40.
Key Words: Relativistic Schrodinger operators; pseudo-relativistic Hamiltonians; generalized eigenfunctions; Riesz potentials; radiation conditions.
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| Tomio Umeda |
Department of Mathematical Sciences
University of Hyogo
Shosha, Himeji 671-2201, Japan
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