Geodesic
Exponential Instability in the Inverse Scattering Problem on the Energy Interval
Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 3, pp. 28-36

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

We consider the inverse scattering problem on the energy interval in three dimensions. We focus on stability and instability questions for this problem. In particular, we prove an exponential instability estimate which shows the optimality, up to the value of the exponent, of the logarithmic stability result obtained by P. Stefanov in 1990 with the use of some special norm for the scattering amplitude at fixed energy.
Keywords: inverse scattering problem, stability estimates, $\varepsilon$-capacity, $\varepsilon$-entropy. 
@article{FAA_2013_47_3_a2,
     author = {M. I. Isaev},
     title = {Exponential {Instability} in the {Inverse} {Scattering} {Problem} on the {Energy} {Interval}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {28--36},
     publisher = {mathdoc},
     volume = {47},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2013_47_3_a2/}
}
TY  - JOUR
AU  - M. I. Isaev
TI  - Exponential Instability in the Inverse Scattering Problem on the Energy Interval
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2013
SP  - 28
EP  - 36
VL  - 47
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2013_47_3_a2/
LA  - ru
ID  - FAA_2013_47_3_a2
ER  - 
%0 Journal Article
%A M. I. Isaev
%T Exponential Instability in the Inverse Scattering Problem on the Energy Interval
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2013
%P 28-36
%V 47
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2013_47_3_a2/
%G ru
%F FAA_2013_47_3_a2
M. I. Isaev. Exponential Instability in the Inverse Scattering Problem on the Energy Interval. Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 3, pp. 28-36. http://geodesic.mathdoc.fr/item/FAA_2013_47_3_a2/