Generalized eigenfunctions of relativistic Schrodinger operators I
| dc.contributor.author | Umeda, Tomio | |
| dc.date.accessioned | 2021-07-20T19:37:12Z | |
| dc.date.available | 2021-07-20T19:37:12Z | |
| dc.date.issued | 2006-10-11 | |
| dc.description.abstract | Generalized eigenfunctions of the 3-dimensional relativistic Schrödinger operator √-Δ+V(x) with |V(x)| ≤ C ⟨x⟩-σ, σ > 1, are considered. We construct the generalized eigenfunctions by exploiting results on the limiting absorption principle. We compute explicitly the integral kernal of (√-Δ -z)-1, z ∈ ℂ \ [0, +∞), which has nothing in common with the integral kernal of (-Δ -z)-1, but the leading term of the integral kernals of the boundary values (√-Δ -λ ∓i0)-1, λ > 0, turn out to be the same, up to a constant, as the integral kernals of the boundary values (-Δ -λ∓i0)-1. This fact enables us to show that the asymptotic behavior, as |x| → +∞, of the generalized eigenfunction of √-Δ + V(x) is equal to the sum of a plane wave and a spherical wave when σ > 3. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 46 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Umeda, T. (2006). Generalized eigenfunctions of relativistic Schrodinger operators I. <i>Electronic Journal of Differential Equations, 2006</i>(127), pp. 1-46. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14000 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2006, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Relativistic Schrodinger operators | |
| dc.subject | Pseudo-relativistic Hamiltonians | |
| dc.subject | Generalized eigenfunctions | |
| dc.subject | Riesz potentials | |
| dc.subject | Radiation conditions | |
| dc.title | Generalized eigenfunctions of relativistic Schrodinger operators I | |
| dc.type | Article |