Richard Ford
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.
Submitted August 24, 1999. Published January 21, 2000.
Math Subject Classifications: 35J10, 35P25, 35R30, 81U40.
Key Words: inverse scattering, Green's functions,
Schrödinger equation, Born approximation, Measure potentials.
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