Riemann-Lebesgue properties of Green's functions with applications to inverse scattering
Saito's method has been applied successfully for measuring potentials with compact support in three dimensions. Also potentials have been reconstructed in the sense of distributions using a weak version of the method. Saito's method does not depend on the decay of the boundary value of the...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2000-01-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2000/07/abstr.html |
| _version_ | 1818066875560493056 |
|---|---|
| author | Richard Ford |
| author_facet | Richard Ford |
| author_sort | Richard Ford |
| collection | DOAJ |
| description | Saito's method has been applied successfully for measuring potentials with compact support in three dimensions. Also potentials have been reconstructed in the sense of distributions using a weak version of the method. Saito's method does not depend on the decay of the boundary value of the resolvent operator, but instead on certain Reimann-Lebesgue type properties of convolutions of the kernel of the unperturbed resolvent. In this paper these properties are extended from three to higher dimensions. We also provide an important application to inverse scattering by extending reconstruction results to measure potentials with unbounded support. |
| first_indexed | 2024-12-10T15:14:44Z |
| format | Article |
| id | doaj.art-dce883fa9eb74b8e8cd63a010e8e26f6 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-10T15:14:44Z |
| publishDate | 2000-01-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-dce883fa9eb74b8e8cd63a010e8e26f62022-12-22T01:43:49ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912000-01-01200007119Riemann-Lebesgue properties of Green's functions with applications to inverse scatteringRichard FordSaito's method has been applied successfully for measuring potentials with compact support in three dimensions. Also potentials have been reconstructed in the sense of distributions using a weak version of the method. Saito's method does not depend on the decay of the boundary value of the resolvent operator, but instead on certain Reimann-Lebesgue type properties of convolutions of the kernel of the unperturbed resolvent. In this paper these properties are extended from three to higher dimensions. We also provide an important application to inverse scattering by extending reconstruction results to measure potentials with unbounded support.http://ejde.math.txstate.edu/Volumes/2000/07/abstr.htmlinverse scatteringGreen's functionsSchrödinger equationBorn approximationMeasure potentials. |
| spellingShingle | Richard Ford Riemann-Lebesgue properties of Green's functions with applications to inverse scattering Electronic Journal of Differential Equations inverse scattering Green's functions Schrödinger equation Born approximation Measure potentials. |
| title | Riemann-Lebesgue properties of Green's functions with applications to inverse scattering |
| title_full | Riemann-Lebesgue properties of Green's functions with applications to inverse scattering |
| title_fullStr | Riemann-Lebesgue properties of Green's functions with applications to inverse scattering |
| title_full_unstemmed | Riemann-Lebesgue properties of Green's functions with applications to inverse scattering |
| title_short | Riemann-Lebesgue properties of Green's functions with applications to inverse scattering |
| title_sort | riemann lebesgue properties of green s functions with applications to inverse scattering |
| topic | inverse scattering Green's functions Schrödinger equation Born approximation Measure potentials. |
| url | http://ejde.math.txstate.edu/Volumes/2000/07/abstr.html |
| work_keys_str_mv | AT richardford riemannlebesguepropertiesofgreensfunctionswithapplicationstoinversescattering |