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

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.

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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

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
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
3. E. L. Korotyaev, “Resonance scattering in a pair of spaces”, Theoret. and Math. Phys., 70:3 (1987), 304–312
4. E. L. Korotyaev, “On the scattering theory of several particles in an external electric field”, Math. USSR-Sb., 60:1 (1988), 177–196
5. E. L. Korotyaev, “On scattering in an external, homogeneous, time-periodic magnetic field”, Math. USSR-Sb., 66:2 (1990), 499–522
6. Moller J., Skibsted E., “Spectral Theory of Time-Periodic Many-Body Systems”, Adv. Math., 188:1 (2004), 137–221
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