Riemann-Lebesgue Properties of Green's Functions with Applications to Inverse Scattering
Date
2000-01-21
Authors
Ford, Richard
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Inverse scattering, Green's functions, Schrdinger equation, Born approximation, Measure potentials
Citation
Ford, R. (2000). Riemann-Lebesgue properties of Green's functions with applications to inverse scattering. <i>Electronic Journal of Differential Equations, 2000</i>(7), pp. 1-19.
Rights
Attribution 4.0 International