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dc.contributor.authorUmeda, Tomio ( )
dc.date.accessioned2021-07-20T19:37:12Z
dc.date.available2021-07-20T19:37:12Z
dc.date.issued2006-10-11
dc.identifier.citationUmeda, T. (2006). Generalized eigenfunctions of relativistic Schrodinger operators I. Electronic Journal of Differential Equations, 2006(127), pp. 1-46.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14000
dc.description.abstractGeneralized eigenfunctions of the 3-dimensional relativistic Schrödinger operator √-Δ+V(x) with |V(x)| ≤ C 〈x〉, 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.formatText
dc.format.extent46 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2006, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectRelativistic Schrodinger operatorsen_US
dc.subjectPseudo-relativistic Hamiltoniansen_US
dc.subjectGeneralized eigenfunctionsen_US
dc.subjectRiesz potentialsen_US
dc.subjectRadiation conditionsen_US
dc.titleGeneralized eigenfunctions of relativistic Schrodinger operators Ien_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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