Geodesic
One-dimensional Schr\"odinger operator with unbounded potential: The pure point spectrum
Funkcionalʹnyj analiz i ego priloženiâ, Tome 24 (1990) no. 3, pp. 14-25.

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     title = {One-dimensional {Schr\"odinger} operator with unbounded potential: {The} pure point spectrum},
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W. Kirsсh; S. A. Molchanov; L. A. Pastur. One-dimensional Schr\"odinger operator with unbounded potential: The pure point spectrum. Funkcionalʹnyj analiz i ego priloženiâ, Tome 24 (1990) no. 3, pp. 14-25. http://geodesic.mathdoc.fr/item/FAA_1990_24_3_a2/

[1] Simon V., Spencer T., “Trace class perturbations and the absence of absolutely continuous spectra”, Commun. Math. Phys., 125 (1989), 113–125 | DOI | MR | Zbl

[2] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR

[3] Gordon A.Ya., “O tochechnom spektre odnomernogo operatora Shredingera”, UMN, 31:4 (1976), 257–258 | MR | Zbl

[4] Gordon A.Ya., Spektralnye svoistva operatorov, approksimiruemykh periodicheskimi, i ubyvanie lakun dlya ogranichennogo potentsiala, Dis. ... kand. fiz.-mat. nauk, MIEM, M., 1988

[5] Pastur L.A., “Spektralnaya teoriya sluchainykh samosopryazhennykh operatorov”, Itogi nauki i tekhniki. Teoriya veroyatnostei, 25, VINITI, M., 1987, 3–67

[6] Fröhlich G., Spencer T., “Absence of diffusion in the Anderson tight-binding model for large disorder or low energy”, Commun. Math. Phys., 88 (1983), 151–189 | DOI | MR

[7] Martinelli F., Scoppolla E., “Introduction to the mathematical theory of Anderson localization”, Rivista Nuovo Cimento, 10 (1987), 2–90 | DOI | MR

[8] Kotani S., “Lyapunov exponent and spectra for one-dimensional random Schrodinger operator”, Contemp. Math., 50 (1986), 277–286 | DOI | MR | Zbl

[9] Simon V., Wolff T., “Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians”, Commun. Pure Appl. Math., 39 (1986), 75–90 | DOI | MR | Zbl

[10] Delyon F., Levy Y., Souillard V., “Anderson localization for one- and quasi-one-dimensional systems”, J. Stat. Phys., 41 (1985), 375–388 | DOI | MR

[11] Goldsheidt I.Ya., Molchanov S.A., Pastur L.A., “Sluchainyi odnomernyi operator Shredingera imeet chisto tochechnyi spektr”, Funktsion. analiz i ego pril., 11:1 (1977), 1–10 | MR | Zbl

[12] Carmona R., “Exponential localization in one dimensional disordered systems”, Duke Math. J., 49 (1982), 191–213 | DOI | MR | Zbl

[13] Fishman S., Grempel D., Prange R., “Chaos, Quantum recurrences and Anderson localization”, Phys. Rev. Lett., 49 (1982), 509–512 | DOI | MR

[14] Kirsch W., Molchanov S., Pastur L., The pure point spectrum of the one-dimensional Schrodinger operator with an unbounded potential, Preprint Ruhr-Universitat Bochum, Ruhr Universitat, Bochum, 1989 | MR

[15] Glazman I.M., Pryamye metody kachestvennogo spektralnogo analiza singulyarnykh differentsialnykh operatorov, Fizmatgiz, M., 1963 | MR

[16] Kramer G., Lidbetter M., Statsionarnye sluchainye protsessy, Mir, M., 1969

[17] Kotani S., “Lyapunov indices determine absolutely continuous spectra of stationary random one-dimensional Schrodinger operator”, Proceedings of Taniguchi Symposium, 1982, North Holland, Amsterdam, 1984, 225–247 | MR | Zbl

[18] Malyshev B.A., Minlos P.A., Gibbsovskie sluchainye polya, Nauka, M., 1985 | MR

[19] Khinchin A.Ya., Tsepnye drobi, Fizmatgiz, M., 1963

[20] Simon V., “Almost-periodic Schrodinger operator. IV. The Maryland model”, Ann. Phys., 159 (1985), 157–183 | DOI | MR | Zbl

[21] Pastur L.A., Figotin A.L., “An exactly soluble model of multidimensional incommensurate structure”, Commun. Math. Phys., 95 (1984), 401–425 | DOI | MR | Zbl