zbMATH — the first resource for mathematics

A pure point spectrum of the stochastic one-dimensional Schrödinger operator. (English) Zbl 0368.34015

34L99 Ordinary differential operators
34F05 Ordinary differential equations and systems with randomness
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
Full Text: DOI
[1] L. A. Pastur, ”Spectra of random Jacobi matrices and Schrödinger equations with random potentials on the whole axis,” Preprint, FTINT Akad. Nauk UkrSSR, Khar’kov (1974).
[2] A. Ya. Gordon, ”On the point spectrum of a one-dimensional Schrödinger operator,” Usp. Mat. Nauk,31, No. 4, 257-258 (1976). · Zbl 0342.34012
[3] E. I. Dinaburg and Ya. G. Sinai, ”On the one-dimensional Schrödinger equation with a quasiperiodic potential,” Funkts. Anal. Prilozhen.,9, No. 4, 8-21 (1975). · Zbl 0357.58011 · doi:10.1007/BF01078168
[4] N. F. Mott and E. A. Davis, Electronic Processes in Non-Crystalline Materials, Oxford Univ. Press (1971).
[5] B. I. Halperin, ”Properties of a particle in a one-dimensional random potential,” Adv. Chem. Phys.,13, 123-178 (1967). · doi:10.1002/9780470140154.ch6
[6] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag (1966). · Zbl 0148.12601
[7] I. Ya. Gol’dshtein and S. A. Molchanov, ”On a problem of Mott,” Dokl. Akad. Nauk SSSR,230, No. 4, 761-764 (1976).
[8] H. P. McKean, Jr., Stochastic Integrals, Academic Press (1969).
[9] B. M. Levitan and I. S. Sargsjan, Introduction to Spectral Theory, Am. Math. Soc. (1974). · Zbl 0302.47036
[10] L. Hörmander, ”Hypoelliptic differential equations of second order,” Matematika,12:2, 88-109 (1968).
[11] K. Ichihara and H. Kunita, ”A classification of second-order degenerate elliptic operators, and its probabilistic characterization,” Z. Wahrsch.,30, No. 3, 235-254 (1974). · Zbl 0326.60097 · doi:10.1007/BF00533476
[12] I. M. Glazman, Direct Methods of Qualitative Spectral Analysis and Singular Differential Operators [in Russian], Fizmatgiz, Moscow (1963). · Zbl 0143.36504
[13] H. Furstenberg, ”Noncommuting random products,” Trans. Am. Math. Soc.,108, No. 3, 337-428 (1963). · Zbl 0203.19102 · doi:10.1090/S0002-9947-1963-0163345-0
[14] M. A. Krasnosel’skii, Positive Solutions of Operator Equations [in Russian], Fizmatgiz, Moscow (1962).
[15] V. S. Korolyuk, S. M. Brodi, and A. F. Turbin, Semi-Markov Processes and Their Application [in Russian], Naukova Dumka, Kiev (1976). · Zbl 0338.60061
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.