Tomio Umeda, Dabi Wei
Abstract:
This article concerns the generalized eigenfunctions of the two-dimensional
relativistic Schrodinger operator
with
,
.
We compute the integral kernels of the boundary values
,
and
prove that the generalized eigenfunctions
are bounded on
,
where
,
and
is the set of eigenvalues of
.
With this fact and the
completeness of the wave operators, we establish the eigenfunction
expansion for the absolutely continuous subspace for
. 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
.
Submitted August 19, 2008. Published October 24, 2008.
Math Subject Classifications: 35P10, 81U05, 47A40.
Key Words: Relativistic Schrodinger operators; generalized eigenfunctions;
pseudo-relativistic Hamiltonians.
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Tomio Umeda Department of Mathematical Science, University of Hyogo Shosha 2167, Himeji 671-2201, Japan email: umeda@sci.u-hyogo.ac.jp | |
Dabi Wei Department of Mechanical and Control Engineering Graduate School of Science and Engineering Tokyo Institute of Technology 2-12-1 S5-22 O-okayama, Meguro-ku, Tokyo 152-8550, Japan email: dabi@ok.ctrl.titech.ac.jp |
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