This article is cited in 15 papers

Exponential Instability in the Inverse Scattering Problem on the Energy Interval

M. I. Isaev<sup>ab

a</sup> Centre de Mathématiques Appliquées, École Polytechnique
^b Moscow Institute of Physics and Technology (State University)

Abstract: 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.

UDC: 517.9

Received: 07.06.2011

DOI: 10.4213/faa3116

 English version: Functional Analysis and Its Applications, 2013, 47:3, 187–194

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