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L. A. Pastur, “The spectral theory of random self-adjoint operators,” Itogi Nauki i Tekh., VINITI, Probability Theory, Vol. 25, 3–67 (1987).
I. Ya. Gol'dsheid, S. A. Molchanov, and L. A. Pastur, “A random one-dimensional Scrödinger operator has a pure point spectrum,” Funkts. Anal. Prilozhen.,11, No. 1, 1–10 (1977).
S. A. Molchanov, “The structure of the eigenfunctions of one-dimensional disordered structures,” Izv. Akad. Nauk SSSR, Ser. Mat.,42, No. 1, 70–103 (1978).
H. Kunz and B. Souillard, “Sur le spectre des opérateurs aux différences finies aléatoires,” Commun. Math. Phys.,78, No. 2, 201–246 (1980).
A. G. Golitsina and S. A. Molchanov, “A multidimensional model of rare random scatters,” Dokl. Akad. Nauk SSSR,294, No. 5, 1302–1306 (1987).
L. A. Malozemov, “The Thouless formula and the absence of an absolutely continuous spectrum for a Schrödinger operator with perturbed random potentials,” Vest. Mosk. Univ. Ser. I Mat., Mekh., No. 6, 3–6 (1988).
L. A. Malozemov, “Eigenvalues imbedded in the continuous spectrum of a perturbed almost periodic operator,” Usp. Mat. Nauk,43, No. 4 (262), 211–212 (1988).
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 3, Scattering Theory, Vol. 4, Analysis of Operators, Academic Press, New York (1980).
F. Delyon, H. Kunz, and B. Souillard, “One-dimensional wave equation in disordered media,” J. Phys. A,16, No. 1, 25–42 (1983).
T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, New York (1966).
L. A. Malozemov, The Spectrum of a One-Dimensional Schrödinger Difference Operator with a Random Nonstationary Potential [in Russian], Dep. VINITI 07.06.88, No. 4498-88 (1988).
L. A. Malozemov, The Spectral Theory of Schrödinger Operators with Random and Asymptotically Almost Periodic Potentials [in Russian], Dissert., Cand. Phys.-Mat. Sci., Moscow (1989).
B. Simon, “Some Jacobi matrices with decaying potential and dense point spectrum,” Commun. Math. Phys.,87, No. 2, 253–258 (1982).
F. Delyon, B. Simon, and B. Souillard, “From power pure point to continuous spectrum in disordered systems,” Ann. Inst. Henri Poincaré.,42, No. 3, 283–309 (1985).
F. Delyon, “Appearance of a purely singular continuous spectrum in a class of random Schrödinger operators,” J. Stat. Phys.,40, No. 516, 621–630 (1985).
Translated from Matematicheskie Zametki, Vol. 50, No. 3, pp. 81–86, September, 1991.
The author is grateful to M. A. Shubin for numerous fruitful discussions and support.
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Malozemov, L.A. Spectrum of a random Schrödinger difference operator. Mathematical Notes of the Academy of Sciences of the USSR 50, 935–938 (1991). https://doi.org/10.1007/BF01156138
- Difference Operator