Tomio Umeda, Dabi Wei
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.
Show me the PDF file (327 KB), TEX file, and other files for this article.
| Tomio Umeda |
Department of Mathematical Science, University of Hyogo
Shosha 2167, Himeji 671-2201, Japan
| 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
Return to the EJDE web page