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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 451, Pages 134–155 (Mi znsl6350)  
This article is cited in 6 scientific papers (total in 6 papers)

Connection of the different types of inverse data for the one-dimensional Schrödinger operator on the half-line

A. S. Mikhaylovab, V. S. Mikhaylovab

a St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, 27, Fontanka, 191023 St. Petersburg, Russia
b Saint Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034 Russia
Full-text PDF (242 kB) Citations (6)
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Abstract: We consider inverse dynamical, spectral, quantum and acoustical scattering problems for the Schrödinger operator on the half line. The goal of the paper is to establish the connections between different types of inverse data for these problems. The central objects which serve as a source for all formulaes are kernels of so-called connecting operators and Krein equations.
Key words and phrases: inverse problem, Schrödinger operator, Boundary Control method, scattering matrix, Weyl function.
Funding agency Grant number
Saint Petersburg State University 11.38.263.2014
Russian Foundation for Basic Research 14-01-00535
14-01-00306
Volkswagen Foundation
The research of Victor Mikhaylov was supported in part by NIR SPbGU 11.38.263.2014 and RFBR 14-01-00535. Alexandr Mikhaylov was supported by RFBR 14-01-00306; A. S. Mikhaylov and V. S. Mikhaylov were partly supported by VW Foundation program “Modeling, Analysis, and Approximation Theory toward application in tomography and inverse problems.”
Received: 02.10.2016
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 226, Issue 6, Pages 779–794
DOI: https://doi.org/10.1007/s10958-017-3566-2
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: English
Citation: A. S. Mikhaylov, V. S. Mikhaylov, “Connection of the different types of inverse data for the one-dimensional Schrödinger operator on the half-line”, Mathematical problems in the theory of wave propagation. Part 46, Zap. Nauchn. Sem. POMI, 451, POMI, St. Petersburg, 2016, 134–155; J. Math. Sci. (N. Y.), 226:6 (2017), 779–794
Citation in format AMSBIB
\Bibitem{MikMik16}
\by A.~S.~Mikhaylov, V.~S.~Mikhaylov
\paper Connection of the different types of inverse data for the one-dimensional Schr\"odinger operator on the half-line
\inbook Mathematical problems in the theory of wave propagation. Part~46
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 451
\pages 134--155
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6350}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3589171}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 226
\issue 6
\pages 779--794
\crossref{https://doi.org/10.1007/s10958-017-3566-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85030221877}
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  • https://www.mathnet.ru/eng/znsl/v451/p134
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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