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Funktsional. Anal. i Prilozhen., 2013, Volume 47, Issue 3, Pages 28–36 (Mi faa3116)  

This article is cited in 6 scientific papers (total in 6 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)

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

DOI: https://doi.org/10.4213/faa3116

Full text: PDF file (176 kB)
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English version:
Functional Analysis and Its Applications, 2013, 47:3, 187–194

Bibliographic databases:

UDC: 517.9
Received: 07.06.2011

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. G. Novikov, “Approximate Lipschitz stability for non-overdetermined inverse scattering at fixed energy”, J. Inverse Ill-Posed Probl., 21:6 (2013), 813–823  crossref  mathscinet  zmath  isi  elib  scopus
    2. M. I. Isaev, R. G. Novikov, “Effectivized Hölder-logarithmic stability estimates for the Gel'fand inverse problem”, Inverse Problems, 30:9 (2014), 095006, 18 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. R. G. Novikov, “An iterative approach to non-overdetermined inverse scattering at fixed energy”, Sb. Math., 206:1 (2015), 120–134  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Hohage T. Weidling F., “Verification of a Variational Source Condition For Acoustic Inverse Medium Scattering Problems”, Inverse Probl., 31:7 (2015), 075006  crossref  mathscinet  zmath  isi  elib  scopus
    5. Novikov R.G., “Explicit Formulas and Global Uniqueness for Phaseless Inverse Scattering in Multidimensions”, J. Geom. Anal., 26:1 (2016), 346–359  crossref  mathscinet  zmath  isi  elib  scopus
    6. Agaltsov A.D., Hohage T., Novikov R.G., “An Iterative Approach to Monochromatic Phaseless Inverse Scattering”, Inverse Probl., 35:2 (2019), 024001  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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