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Funktsional. Anal. i Prilozhen.:

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Funktsional. Anal. i Prilozhen., 1975, Volume 9, Issue 4, Pages 8–21 (Mi faa2277)  

This article is cited in 22 scientific papers (total in 24 papers)

The one-dimensional Schrödinger equation with a quasiperiodic potential

E. I. Dinaburg, Ya. G. Sinai

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English version:
Functional Analysis and Its Applications, 1975, 9:4, 279–289

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Received: 24.05.1974

Citation: E. I. Dinaburg, Ya. G. Sinai, “The one-dimensional Schrödinger equation with a quasiperiodic potential”, Funktsional. Anal. i Prilozhen., 9:4 (1975), 8–21; Funct. Anal. Appl., 9:4 (1975), 279–289

Citation in format AMSBIB
\by E.~I.~Dinaburg, Ya.~G.~Sinai
\paper The one-dimensional Schr\"odinger equation with a quasiperiodic potential
\jour Funktsional. Anal. i Prilozhen.
\yr 1975
\vol 9
\issue 4
\pages 8--21
\jour Funct. Anal. Appl.
\yr 1975
\vol 9
\issue 4
\pages 279--289

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    This publication is cited in the following articles:
    1. E. D. Belokolos, “Quantum particle in a one-dimensional deformed lattice. Estimates of the gaps in the spectrum”, Theoret. and Math. Phys., 25:3 (1975), 1176–1184  mathnet  crossref  mathscinet
    2. B. A. Dubrovin, V. B. Matveev, S. P. Novikov, “Non-linear equations of Korteweg–de Vries type, finite-zone linear operators, and Abelian varieties”, Russian Math. Surveys, 31:1 (1976), 59–146  mathnet  crossref  mathscinet  zmath
    3. I. Ya. Gol'dsheid, S. A. Molchanov, L. A. Pastur, “A pure point spectrum of the stochastic one-dimensional Schrödinger operator”, Funct. Anal. Appl., 11:1 (1977), 1–8  mathnet  crossref  mathscinet  zmath
    4. M. A. Shubin, “Almost periodic functions and partial differential operators”, Russian Math. Surveys, 33:2 (1978), 1–52  mathnet  crossref  mathscinet  zmath
    5. M. A. Shubin, “The spectral theory and the index of elliptic operators with almost periodic coefficients”, Russian Math. Surveys, 34:2 (1979), 109–157  mathnet  crossref  mathscinet  zmath
    6. B. M. Levitan, “On the closure of the set of finite-zone potentials”, Math. USSR-Sb., 51:1 (1985), 67–89  mathnet  crossref  mathscinet  zmath
    7. Ya. G. Sinai, “Structure of the spectrum of the Schrödinger operator with almost-periodic potential in the vicinity of its left edge”, Funct. Anal. Appl., 19:1 (1985), 34–39  mathnet  crossref  mathscinet  zmath  isi
    8. L. A. Malozemov, “On the eigenvalues of a perturbed almost periodic operator that are immersed in the continuous spectrum”, Russian Math. Surveys, 43:4 (1988), 219–220  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. E. I. Dinaburg, “Stark effect for a difference Schrödinger operator”, Theoret. and Math. Phys., 78:1 (1989), 50–57  mathnet  crossref  mathscinet  isi
    10. S. Ya. Zhitomirskaya, “Spectral properties of one-dimensional almost periodic operators”, Russian Math. Surveys, 46:2 (1991), 260–261  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. E. O. Lokutsievskaya, “Structure of spectrum of Schrödinger operator with quasiperiodic potential near the ground state. The discrete and continuous cases”, Theoret. and Math. Phys., 87:2 (1991), 478–488  mathnet  crossref  mathscinet  zmath  isi
    12. A. M. Samoilenko, “N. N. Bogolyubov and non-linear mechanics”, Russian Math. Surveys, 49:5 (1994), 109–154  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. S. P. Novikov, L. A. Bunimovich, A. M. Vershik, B. M. Gurevich, E. I. Dinaburg, G. A. Margulis, V. I. Oseledets, S. A. Pirogov, K. M. Khanin, N. N. Chentsova, “Yakov Grigor'evich Sinai (on his sixtieth birthday)”, Russian Math. Surveys, 51:4 (1996), 765–778  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    14. E. I. Dinaburg, “Some questions of the spectral theory of discrete operators with quasiperiodic coefficients”, Russian Math. Surveys, 52:3 (1997), 451–499  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    15. V. V. Belov, O. S. Dobrokhotov, S. Yu. Dobrokhotov, “Isotropic Tori, Complex Germ and Maslov Index, Normal Forms and Quasimodes of Multidimensional Spectral Problems”, Math. Notes, 69:4 (2001), 437–466  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. V. V. Belov, S. Yu. Dobrokhotov, V. A. Maksimov, “Explicit Formulas for Generalized Action–Angle Variables in a Neighborhood of an Isotropic Torus and Their Application”, Theoret. and Math. Phys., 135:3 (2003), 765–791  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    17. J. Bourgain, “Recent progress on quasi-periodic lattice Schrödinger operators and Hamiltonian PDEs”, Russian Math. Surveys, 59:2 (2004), 231–246  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    18. M. Aizenman, S. Warzel, “Persistence under weak disorder of AC spectra of quasi-periodic Schrödinger operators on trees graphs.”, Mosc. Math. J., 5:3 (2005), 499–506  mathnet  mathscinet  zmath
    19. D. V. Zakharov, “Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation”, Theoret. and Math. Phys., 153:1 (2007), 1388–1397  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    20. A. A. Fedotov, “Adiabatic almost-periodic Schrödinger operators”, J. Math. Sci. (N. Y.), 173:3 (2011), 299–319  mathnet  crossref
    21. A. A. Fedotov, “Monodromization method in the theory of almost-periodic equations”, St. Petersburg Math. J., 25:2 (2014), 303–325  mathnet  crossref  mathscinet  zmath  isi  elib
    22. A. I. Bufetov, B. M. Gurevich, K. M. Khanin, F. Cellarosi, “The Abel Prize award to Ya. G. Sinai”, Russian Math. Surveys, 69:5 (2014), 931–956  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    23. Zhang X., “Dynamics of Nonautonomous Ordinary Differential Equations With Quasi-Periodic Coefficients”, Int. J. Bifurcation Chaos, 27:6 (2017), 1750092  crossref  isi
    24. Bjerklov K., “On Some Generalizations of Skew-Shifts on T-2”, Ergod. Theory Dyn. Syst., 39:1 (2019), 19–61  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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