Geodesic
A~test for the~existence of exceptional points in the~Faddeev scattering problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 1, pp. 87-103

Voir la notice de l'article provenant de la source Math-Net.Ru

Exceptional points are values of the spectral parameter for which the homogeneous Faddeev scattering problem has a nontrivial solution. We formulate a criterion for existence of exceptional points that belong to a given path. For this, we use measurements at the endpoints of the path. We also study the existence or absence of exceptional points for small perturbations of conductive potentials of arbitrary shape and show that problems with absorbing potentials do not have exceptional points in a neighborhood of the origin.
Keywords: exceptional point, Faddeev Green's function, conductive potential. 
@article{TMF_2017_190_1_a5,
     author = {E. L. Lakshtanov and B. R. Vainberg},
     title = {A~test for the~existence of exceptional points in {the~Faddeev} scattering problem},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {87--103},
     publisher = {mathdoc},
     volume = {190},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_190_1_a5/}
}
TY  - JOUR
AU  - E. L. Lakshtanov
AU  - B. R. Vainberg
TI  - A~test for the~existence of exceptional points in the~Faddeev scattering problem
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2017
SP  - 87
EP  - 103
VL  - 190
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2017_190_1_a5/
LA  - ru
ID  - TMF_2017_190_1_a5
ER  - 
%0 Journal Article
%A E. L. Lakshtanov
%A B. R. Vainberg
%T A~test for the~existence of exceptional points in the~Faddeev scattering problem
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2017
%P 87-103
%V 190
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2017_190_1_a5/
%G ru
%F TMF_2017_190_1_a5
E. L. Lakshtanov; B. R. Vainberg. A~test for the~existence of exceptional points in the~Faddeev scattering problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 1, pp. 87-103. http://geodesic.mathdoc.fr/item/TMF_2017_190_1_a5/