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Zapiski Nauchnykh Seminarov POMI, 1998, Volume 250, Pages 161–190 (Mi znsl649)  

This article is cited in 1 scientific paper (total in 1 paper)

Abel–Lidskii bases in non-selfadjoint inverse boundary problem

Ya. V. Kuryleva, M. Lassasb

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Rolf Nevanlinna Institute, Department of Mathematics and Statistics, University of Helsinki
Full-text PDF (352 kB) Citations (1)
Abstract: Let $M$ be a manifold with bondary $\partial M\ne\varnothing$. Let $A$ be a 2-nd order elliptic PDO on $M$. Denote by $R_\lambda(x,y)$, $x$, $y\in M$, $\lambda\in\mathbb C\setminus\sigma(A)$ the Schwartz kernel of $(A-\lambda I)^{-1}$. We consider the Gel'fand inverse boundary problem of the reconstruction of $(M,A)$ via given $R_\lambda(x,y)$, $x$, $y\in\partial M$, $\lambda\in\mathbb C$. We prove that if the main symbol of $A$ satisfies some geometrical condition (Bardos–Lebeau–Rauch condition) then these data determine $M$ uniquely and $A$ to within the group of the generalized gauge transformations on $M$. The above mentioned geometric condition means, roughly speaking, that any geodesics (in the metric generated by $A$) leaves $M$.
Received: 16.10.1997
English version:
Journal of Mathematical Sciences (New York), 2000, Volume 102, Issue 4, Pages 4237–4257
DOI: https://doi.org/10.1007/BF02673855
Bibliographic databases:
UDC: 517.946
Language: Russian
Citation: Ya. V. Kurylev, M. Lassas, “Abel–Lidskii bases in non-selfadjoint inverse boundary problem”, Mathematical problems in the theory of wave propagation. Part 27, Zap. Nauchn. Sem. POMI, 250, POMI, St. Petersburg, 1998, 161–190; J. Math. Sci. (New York), 102:4 (2000), 4237–4257
Citation in format AMSBIB
\Bibitem{KurLas98}
\by Ya.~V.~Kurylev, M.~Lassas
\paper Abel--Lidskii bases in non-selfadjoint inverse boundary problem
\inbook Mathematical problems in the theory of wave propagation. Part~27
\serial Zap. Nauchn. Sem. POMI
\yr 1998
\vol 250
\pages 161--190
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl649}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1701865}
\zmath{https://zbmath.org/?q=an:0984.58009}
\transl
\jour J. Math. Sci. (New York)
\yr 2000
\vol 102
\issue 4
\pages 4237--4257
\crossref{https://doi.org/10.1007/BF02673855}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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