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.

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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. 
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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/

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