Generalized eigenfunctions of relativistic Schroedinger operators in two dimensions
| dc.creator | Umeda, Tomio | |
| dc.creator | Wei, Dabi | |
| dc.date | 2008-08-26 | |
| dc.date.accessioned | 2026-07-07T09:58:27Z | |
| dc.date.available | 2026-07-07T09:58:27Z | |
| dc.description | Generalized eigenfunctions of the two-dimensional relativistic Schrödinger operator $H=\sqrt{-Δ}+V(x)$ with $|V(x)|\leq C< x>^{-σ}$, $σ>3/2$, are considered. We compute the integral kernels of the boundary values $R_0^\pm(λ)=(\sqrt{-Δ}-(λ\pm i0))^{-1}$, and prove that the generalized eigenfunctions $ϕ^\pm(x,k)$ are bounded on $R_x^2\times\{k | a\leq |k|\leq b\}$, where $[a,b]\subset(0,\infty)\backslashσ_p(H)$, and $σ_p(H)$ is the set of eigenvalues of $H$. With this fact and the completeness of the wave operators, we establish the eigenfunction expansion for the absolutely continuous subspace for $H$. 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 $σ>2$. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/0808.3450 | |
| dc.identifier | http://arxiv.org/abs/0808.3450 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167720 | |
| dc.subject | Spectral Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35P10; 81U05 | |
| dc.title | Generalized eigenfunctions of relativistic Schroedinger operators in two dimensions | |
| dc.type | text |