RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Journal history

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Tr. Mosk. Mat. Obs.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Tr. Mosk. Mat. Obs., 2014, Volume 75, Issue 2, Pages 159–180 (Mi mmo562)  

This article is cited in 2 scientific papers (total in 2 papers)

Noncommutative geometry and the tomography of manifolds

M. I. Belishevab, M. N. Demchenkoab, A. N. Popova

a Saint Petersburg State University
b St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences

Abstract: The tomography of manifolds describes a range of inverse problems in which we seek to reconstruct a Riemannian manifold from its boundary data (the “Dirichlet–Neumann” mapping, the reaction operator, and others). Different types of data correspond to physically different situations: the manifold is probed by electric currents or by acoustic or electromagnetic waves. In our paper we suggest a unified approach to these problems, using the ideas of noncommutative geometry. Within the framework of this approach, the underlying manifold for the reconstruction is obtained as the spectrum of an adequate Banach algebra determined by the boundary data.

Full text: PDF file (392 kB)
References: PDF file   HTML file

English version:
Transactions of the Moscow Mathematical Society, 2014, 75, 133–149

UDC: 517.958
MSC: 35R30, 46L60, 58B34, 93B28, 35Q61
Received: 28.02.2014

Citation: M. I. Belishev, M. N. Demchenko, A. N. Popov, “Noncommutative geometry and the tomography of manifolds”, Tr. Mosk. Mat. Obs., 75, no. 2, MCCME, M., 2014, 159–180; Trans. Moscow Math. Soc., 75 (2014), 133–149

Citation in format AMSBIB
\Bibitem{BelDemPop14}
\by M.~I.~Belishev, M.~N.~Demchenko, A.~N.~Popov
\paper Noncommutative geometry and the tomography of manifolds
\serial Tr. Mosk. Mat. Obs.
\yr 2014
\vol 75
\issue 2
\pages 159--180
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo562}
\elib{http://elibrary.ru/item.asp?id=23780161}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2014
\vol 75
\pages 133--149
\crossref{https://doi.org/10.1090/S0077-1554-2014-00239-9}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960105450}


Linking options:
  • http://mi.mathnet.ru/eng/mmo562
  • http://mi.mathnet.ru/eng/mmo/v75/i2/p159

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. M. I. Belishev, “Boundary control and tomography of Riemannian manifolds (the BC-method)”, Russian Math. Surveys, 72:4 (2017), 581–644  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. I M. Belishev, V A. Kaplun, “Eikonal algebra on a graph of simple structure”, Eurasian J. Math. Comput. Appl., 6:3 (2018), 4–33  crossref  isi
  • Trudy Moskovskogo Matematicheskogo Obshchestva
    Number of views:
    This page:182
    Full text:93
    References:14

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019