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Mat. Sb. (N.S.), 1984, Volume 124(166), Number 3(7), Pages 431–446 (Mi msb2060)  

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

On the eigenfunctions of the monodromy operator of the Schrödinger operator with a time-periodic potential

E. L. Korotyaev


Abstract: It is shown that the eigenfunctions of the monodromy operator of the Schrödinger operator (with a potential periodic in time and rapidly decreasing in the space variables) decay in the space variables faster than any power.
The spectrum of the monodromy operator is also investigated. It is proved that 1) the monodromy operator has no singular continuous spectrum; and 2) the total number of eigenfunctions of the monodromy operator (counting multiplicity) is finite.
Bibliography: 19 titles.

Full text: PDF file (841 kB)
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English version:
Mathematics of the USSR-Sbornik, 1985, 52:2, 423–438

Bibliographic databases:

UDC: 517.9
MSC: Primary 35J10, 35P25; Secondary 81F10
Received: 27.04.1983

Citation: E. L. Korotyaev, “On the eigenfunctions of the monodromy operator of the Schrödinger operator with a time-periodic potential”, Mat. Sb. (N.S.), 124(166):3(7) (1984), 431–446; Math. USSR-Sb., 52:2 (1985), 423–438

Citation in format AMSBIB
\Bibitem{Kor84}
\by E.~L.~Korotyaev
\paper On the eigenfunctions of the monodromy operator of the Schr\"odinger operator with a~time-periodic potential
\jour Mat. Sb. (N.S.)
\yr 1984
\vol 124(166)
\issue 3(7)
\pages 431--446
\mathnet{http://mi.mathnet.ru/msb2060}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=752229}
\zmath{https://zbmath.org/?q=an:0582.35030|0566.35034}
\transl
\jour Math. USSR-Sb.
\yr 1985
\vol 52
\issue 2
\pages 423--438
\crossref{https://doi.org/10.1070/SM1985v052n02ABEH002898}


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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. E. L. Korotyaev, “Factorization of three-particle $S$ matrix at high energies”, Theoret. and Math. Phys., 63:3 (1985), 584–588  mathnet  crossref  mathscinet  isi
    2. E. L. Korotyaev, “Scattering theory for a three-particle system with two-body interactions periodic in time”, Theoret. and Math. Phys., 62:2 (1985), 163–171  mathnet  crossref  mathscinet  isi
    3. E. L. Korotyaev, “Resonance scattering in a pair of spaces”, Theoret. and Math. Phys., 70:3 (1987), 304–312  mathnet  crossref  mathscinet  isi
    4. E. L. Korotyaev, “On the scattering theory of several particles in an external electric field”, Math. USSR-Sb., 60:1 (1988), 177–196  mathnet  crossref  mathscinet
    5. E. L. Korotyaev, “On scattering in an external, homogeneous, time-periodic magnetic field”, Math. USSR-Sb., 66:2 (1990), 499–522  mathnet  crossref  mathscinet  zmath  isi
    6. Moller J., Skibsted E., “Spectral Theory of Time-Periodic Many-Body Systems”, Adv. Math., 188:1 (2004), 137–221  crossref  mathscinet  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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