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Funktsional'nyi Analiz i ego Prilozheniya, 2013, Volume 47, Issue 3, Pages 28–36
DOI: https://doi.org/10.4213/faa3116 (Mi faa3116) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Exponential Instability in the Inverse Scattering Problem on the Energy Interval

M. I. Isaevab

a Centre de Mathématiques Appliquées, École Polytechnique
b Moscow Institute of Physics and Technology (State University)
Full-text PDF (176 kB) Citations (14)
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DOI: https://doi.org/10.4213/faa3116
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.
Received: 07.06.2011
English version:
Functional Analysis and Its Applications, 2013, Volume 47, Issue 3, Pages 187–194
DOI: https://doi.org/10.1007/s10688-013-0025-9
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: M. I. Isaev, “Exponential Instability in the Inverse Scattering Problem on the Energy Interval”, Funktsional. Anal. i Prilozhen., 47:3 (2013), 28–36; Funct. Anal. Appl., 47:3 (2013), 187–194
Citation in format AMSBIB
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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