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Zapiski Nauchnykh Seminarov POMI, 2004, Volume 315, Pages 96–101 (Mi znsl740)  
This article is cited in 1 scientific paper (total in 1 paper)

Inverse problem for the discrete periodic Schrödinger operator

E. Korotyaeva, A. Kutsenkobc

a Humboldt-Universität zu Berlin, Institut für Mathematik
b Saint-Petersburg State University
c Universität Potsdam Institut für Mathematik
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Abstract: We study the isospectral sets for the discrete 1D Schrödinger operator on $\mathbb Z$ with a N+1 periodic potential. We show that for small odd potentials the isospectral set consists of $2^{(N+1)/2}$ elements, while for the large potentials the isospectral set consists of $(N+1)!$ elements. Moreover, the asymptotics of the end of the spectrum of the Schrödinger operator for small (and large) potentials are determined.
Received: 20.04.2004
English version:
Journal of Mathematical Sciences (New York), 2006, Volume 134, Issue 4, Pages 2292–2294
DOI: https://doi.org/10.1007/s10958-006-0104-z
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: E. Korotyaev, A. Kutsenko, “Inverse problem for the discrete periodic Schrödinger operator”, Investigations on linear operators and function theory. Part 32, Zap. Nauchn. Sem. POMI, 315, POMI, St. Petersburg, 2004, 96–101; J. Math. Sci. (N. Y.), 134:4 (2006), 2292–2294
Citation in format AMSBIB
\Bibitem{KorKut04}
\by E.~Korotyaev, A.~Kutsenko
\paper Inverse problem for the discrete periodic Schr\"odinger operator
\inbook Investigations on linear operators and function theory. Part~32
\serial Zap. Nauchn. Sem. POMI
\yr 2004
\vol 315
\pages 96--101
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl740}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2114017}
\zmath{https://zbmath.org/?q=an:1084.47023}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 134
\issue 4
\pages 2292--2294
\crossref{https://doi.org/10.1007/s10958-006-0104-z}
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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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