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Almost periodic Schrödinger operators. I: Limit periodic potentials. (English) Zbl 0484.35069


MSC:

35P25 Scattering theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
81Q15 Perturbation theories for operators and differential equations in quantum theory
47A40 Scattering theory of linear operators
47B25 Linear symmetric and selfadjoint operators (unbounded)
35B15 Almost and pseudo-almost periodic solutions to PDEs

Citations:

Zbl 0477.34018
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References:

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[3] Avron, J., Simon, B.: In preparation
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[7] Deift, P.: Private communication
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[13] Johnson, R.: In preparation
[14] Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer 1966 · Zbl 0148.12601
[15] Kovanlenko, V., Semenov, Yu.: Russ. Math. Surv.33, 119-157 (1978) · Zbl 0413.47011
[16] Magnus, W., Winkler, S.: Hill’s equation. New York: Interscience 1966 · Zbl 0158.09604
[17] Moser, J.: An example of a Schrödinger equation with almost periodic potential and nowhere dense spectrum. ETH (preprint) · Zbl 0477.34018
[18] Moser, J.: Private communication
[19] Pastur, L.: Commun. Math. Phys.75, 179-186 (1980) · Zbl 0429.60099
[20] Reed, M., Simon, B.: Methods of modern mathematical physics. I. Functional analysis. London, New York: Academic Press 1972 · Zbl 0242.46001
[21] Reed, M., Simon, B.: Methods of modern mathematical physics. IV. Analysis of operators. London, New York: Academic Press 1978 · Zbl 0401.47001
[22] Simon, B.: Ann. Inst. H. Poincaré A24, 91-93 (1976)
[23] Simon, B.: Schrödinger semigroups (in preparation)
[24] Thomas, L.: Commun. Math. Phys.33, 335-343 (1973)
[25] Trubowitz, E.: Commun. Pure Appl. Math.30, 321-337 (1977) · Zbl 0403.34022
[26] Grossmann, A.: Statistical mechanics and field theory. Sen, R.N., Weil, C. (eds.). Jerusalem: Israel University Press 1972
[27] Blount, E.I.: Solid State Physics13. London, New York: Academic Press 1961
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