Spectral properties of the monodromy matrix for Harper equation

Vladimir Buslaev; Alexander Fedotov

Journées équations aux dérivées partielles (1996)

  • Volume: 1996, page 1-11
  • ISSN: 0752-0360

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Buslaev, Vladimir, and Fedotov, Alexander. "Spectral properties of the monodromy matrix for Harper equation." Journées équations aux dérivées partielles 1996 (1996): 1-11. <http://eudml.org/doc/93329>.

@article{Buslaev1996,
author = {Buslaev, Vladimir, Fedotov, Alexander},
journal = {Journées équations aux dérivées partielles},
keywords = {Harper equation; monodromy matrix; spectral properties; entire analytic solutions; asymptotic behaviour; minimal solutions},
language = {eng},
pages = {1-11},
publisher = {Ecole polytechnique},
title = {Spectral properties of the monodromy matrix for Harper equation},
url = {http://eudml.org/doc/93329},
volume = {1996},
year = {1996},
}

TY - JOUR
AU - Buslaev, Vladimir
AU - Fedotov, Alexander
TI - Spectral properties of the monodromy matrix for Harper equation
JO - Journées équations aux dérivées partielles
PY - 1996
PB - Ecole polytechnique
VL - 1996
SP - 1
EP - 11
LA - eng
KW - Harper equation; monodromy matrix; spectral properties; entire analytic solutions; asymptotic behaviour; minimal solutions
UR - http://eudml.org/doc/93329
ER -

References

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  1. [BS] J. Bellissard, B. Simon, Cantor spectrum for the almost Mathieu equation, Journal of functional analysis 48 No 3 (1982). Zbl0516.47018MR84h:81019
  2. [BF1] V. Buslaev, A. Fedotov, The functional structure of a monodromy matrix for Harper equation, Operator Theory : Advances and Applications 70 (1994), 321-342. Zbl0816.34058MR96f:34004
  3. [BF2] V. Buslaev, A. Fedotov, On a class of matrices related to Harper equation, Reports of Mittag-Leffler Institute 19 (1993), 1-37. 
  4. [BF3] V. Buslaev, A. Fedotov, Complex WKB method for Harper equation. I, Algebra and Analysis (in russian, transl.in english: in St. Petersburg Jour. of Math.) 6 No 3 (1994), 59-83. Zbl0821.34062MR96f:34005
  5. [BF4] V. Buslaev, A. Fedotov, Monodromization and Harper equation, Equations aux dérivées partielles. Ecole Polytechnique, Paris, France (1994), XXI-1-XXI-21. Zbl0880.34082MR95i:81043
  6. [BF5] V. Buslaev, A. Fedotov, Bloch solutions of difference equations, Algebra and Analysis (in russian, engl. translation in St. Petersburg Jour. of Math.) 7 No 4 (1995), 74-121. Zbl0847.39002MR96m:47060
  7. [BF6] V. Buslaev, A. Fedotov, Harper equation: Monodromization without semi-classics, Algebra and Analysis (in russian, engl. translation in St. Petersburg Jour. of Math.) 8 No 2 (1996), 75-109. 
  8. [BF7] V. Buslaev, A. Fedotov, Harper equation: Asymptotics of entire solutions for big values of the spectral parameter, to appear. 
  9. [HS] B. Helffer, J. Sjöstrand, Analyse semi-classique pour l'équation de Harper, Mémoire de la SMF 34 (1988). Zbl0714.34130
  10. [H] D. Hofstadter, Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields, Phys. Rev. B 14 (1976), 2239-2249. 

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