Generalized Backscattering and the Lax-Phillips Transform

Melrose, Richard, and Uhlmann, Gunther. "Generalized Backscattering and the Lax-Phillips Transform." Serdica Mathematical Journal 34.1 (2008): 355-372. <http://eudml.org/doc/281531>.

@article{Melrose2008,
abstract = {2000 Mathematics Subject Classification: 35P25, 35R30, 58J50.Using the free-space translation representation (modified Radon transform) of Lax and Phillips in odd dimensions, it is shown that the generalized backscattering transform (so outgoing angle w = Sq in terms of the incoming angle with S orthogonal and Id-S invertible) may be further restricted to give an entire, globally Fredholm, operator on appropriate Sobolev spaces of potentials with compact support. As a corollary we show that the modified backscattering map is a local isomorphism near elements of a generic set of potentials.},
author = {Melrose, Richard, Uhlmann, Gunther},
journal = {Serdica Mathematical Journal},
keywords = {Radon Transform; Fredholm Family; Holomorphy; Potential Scattering; Inversion; backscattering; Radon transform; Fredholm family; holomorphy; potential scattering; inversion},
language = {eng},
number = {1},
pages = {355-372},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Generalized Backscattering and the Lax-Phillips Transform},
url = {http://eudml.org/doc/281531},
volume = {34},
year = {2008},
}

TY - JOUR
AU - Melrose, Richard
AU - Uhlmann, Gunther
TI - Generalized Backscattering and the Lax-Phillips Transform
JO - Serdica Mathematical Journal
PY - 2008
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 34
IS - 1
SP - 355
EP - 372
AB - 2000 Mathematics Subject Classification: 35P25, 35R30, 58J50.Using the free-space translation representation (modified Radon transform) of Lax and Phillips in odd dimensions, it is shown that the generalized backscattering transform (so outgoing angle w = Sq in terms of the incoming angle with S orthogonal and Id-S invertible) may be further restricted to give an entire, globally Fredholm, operator on appropriate Sobolev spaces of potentials with compact support. As a corollary we show that the modified backscattering map is a local isomorphism near elements of a generic set of potentials.
LA - eng
KW - Radon Transform; Fredholm Family; Holomorphy; Potential Scattering; Inversion; backscattering; Radon transform; Fredholm family; holomorphy; potential scattering; inversion
UR - http://eudml.org/doc/281531
ER -