@article{AIHPA_1985__42_4_383_0,
author = {Kirsch, W. and Kotani, S. and Simon, Barry},
title = {Absence of absolutely continuous spectrum for some one dimensional random but deterministic Schr\"odinger operators},
journal = {Annales de l'I.H.P. Physique th\'eorique},
volume = {43},
year = {1985},
pages = {383-406},
mrnumber = {801236},
zbl = {0581.60052},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPA_1985__42_4_383_0}
}
Kirsch, W.; Kotani, S.; Simon, B. Absence of absolutely continuous spectrum for some one dimensional random but deterministic Schrödinger operators. Annales de l'I.H.P. Physique théorique, Tome 43 (1985) pp. 383-406. http://gdmltest.u-ga.fr/item/AIHPA_1985__42_4_383_0/
[1] and , Almost periodic Schrödinger operators, II. The integrated density of states, Duke Math. J., t. 50, 1983, p. 369-391. | MR 700145 | Zbl 0544.35030
[2] , and , A metal-insulator transition for the almost Mathieu model, Commun. Math. Phys., t. 88, 1983, p. 207-234. | MR 696805 | Zbl 0542.35059
[3] and , Subharmonicity of the Lyaponov index, Duke Math. J., t. 50, 1983, p. 551-560. | MR 705040 | Zbl 0518.35027
[4] and , Potential Scattering, North Holland, Amsterdam, 1965. | MR 191316 | Zbl 0141.23202
[5] and , Inverse Scattering on the Line, Comm. Pure Appl. Math., t. 32, 1979, p. 121-251. | MR 512420 | Zbl 0388.34005
[6] and , On the one dimensional Schrödinger equation with quasi-periodic potential, Funk Anal. i Pril., t. 9, 1975, p. 8-21. | MR 470318 | Zbl 0333.34014
[7] , and , A pure point spectrum of the stochastic and one dimensional Schrödinger equation, Funct. Anal. Appl., t. 11, 1977, p. 1-10. | MR 470515 | Zbl 0368.34015
[8] and , The Stark ladder and other one-dimensional external field problems, Commun. Math. Phys., t. 80, 1981, p. 23. | MR 623150 | Zbl 0473.47037
[9] , Discriminant, transmission coefficients and stability bands of Hill's equation, J. Math. Phys., to appear. | Zbl 0558.34026
[10] , On a class of random Schrödinger operators, to appear in Adv. Appl. Math. | MR 789852 | Zbl 0578.60059
[11] , , On the spectrum of Schrödinger operators with a random potential: Commun. Math. Phys., t. 85, 1982, p. 329-350. | MR 678150 | Zbl 0506.60058
[12] , , On the ergodic properties of the spectrum of general random operators: J. Reine Angew. Math., t. 334, 1982, p. 141-156. | MR 667454 | Zbl 0476.60058
[13] , Lyaponov Indices Determine Absolutely Continuous Spectra of Stationary Random One-Dimensional Schrödinger Operators, Proc. Stoch. Anal., Kyoto, 1982. | Zbl 0549.60058
[14] , Support Theorems for Random Schrödinger Operators, Commun. Math. Phys., to appear. | MR 778625 | Zbl 0573.60054
[15] and , Sur le spectre des opérateurs aux différences finies aléatoires, Commun. Math. Phys., t. 78, 1980, p. 201-246. | MR 597748 | Zbl 0449.60048
[16] and , Hill's Equation, Interscience, 1966; Dover Edition available. | Zbl 0158.09604
[17] and , The theory of impurity conduction, Adv. in Physics, t. 10, 1961, p. 107-155.
[18] , Inverse scattering by a local impurity in a periodic potential in one dimension. J. Math. Phys., t. 24, 1983, p. 2152. | MR 713548 | Zbl 0524.34026
[19] and , Methods of modern mathematical physics. III. Scattering theory, Academic Press, New York, 1979. | MR 529429 | Zbl 0405.47007
[20] and , Methods of modern mathematical physics. IV. Analysis of operators, Academic Press, New York, 1978. | MR 493421 | Zbl 0401.47001
[21] , Kotani theory for one dimensional stochastic Jacobi matrices. Comm. Math. Phys., t. 89, 1983, p. 227. | MR 709464 | Zbl 0534.60057
[22] and , Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955. | MR 69338 | Zbl 0064.33002
[23] and , Linear Operators, Vol. II, Wiley, New York, 1963. | MR 188745 | Zbl 0128.34803
[24] , Schrödinger operators with singular potentials. Israel J. Math., t. 13, 1973, p. 135-148. | MR 333833 | Zbl 0246.35025
[25] and , On the essential selfadjointness of stochastic Schrödinger operators, Duke Math. J., t. 50, 1983, p. 1255-1260. | MR 726328 | Zbl 0543.60069