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Singular continuous spectrum for a class of almost periodic Jacobi matrices
Author(s):
Joseph
Avron;
Barry
Simon
Journal:
Bull. Amer. Math. Soc.
6
(1982),
81-85.
MSC (1980):
Primary 47A10, 47A25;
Secondary 81Cxx
MathSciNet review:
634437
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Additional information
References:
- 1.
- G. André and S. Aubry, Analyticity breaking and Anderson localization in incommensurate lattices, Ann. Israel Phys. Soc. 3 (1980), 133. MR 626837
- 2.
- S. Aubry, The new concept of transition by breaking of analyticity, Solid State Sci. 8 (1978), 264. MR 522493
- 3.
- J. Avron and B. Simon, Almost periodic Schrödinger operators. II. The density of states and the André-Aubry Theorem (in preparation).
- 4.
- J. M. Berezanski, Expansions in eigenfunctions of self-adjoint operators, Transl. Math. Monographs, vol. 17, Amer. Math. Soc., Providence, R. I., 1968. MR 222718
- 5.
- A. Ya. Gordon, On the point spectrum of the one dimensional Schrödinger operator, Uspehi. Math. Nauk. 31 (1976), 257. MR 458247
- 6.
- R. Johnson, The recurrent Hill's equation, U.S.C. preprint.
- 7.
- V. I. Oseledec, A multiplicative ergodic theorem. Lyaponov characteristic numbers for dynamical systems, Trudy. Mosk. at. Obšč. 19 (1968), 679. MR 240280
- 8.
- L. Pasteur and M. Benderskii, On the spectrum of the one-dimensional Schrödinger equation with a random potential, Mat. U.S.S.R. Sb. 11 (1970), 245.
- 9.
- D. Pearson, Singular continuous measures in scattering theory, Comm. Math. Phys. 60 (1978), 13-36. MR 484145
- 10.
- M. Reed and B. Simon, Methods of modern mathematical physics. IV. Analysis of operators, Academic Press, New York, 1978. MR 751959
- 11.
- D. Ruelle, Ergodic theory of differentiate dynamical systems, Inst. Hautes Études Sci. Publ. Math. 50 (1979), 275. MR 556846
- 12.
- M. Shubin, Density of states for self-adjoint elliptic operators with almost periodic coefficients, Trudy Sem. Petrovkii 3 (1978), 243.
- 13.
- D. Thouless, A relation between the density of states and range of localization for one dimensional random system, J.Phys. C 5 (1972), 77-81.
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Additional Information:
DOI:
10.1090/S0273-0979-1982-14971-0
PII:
S 0273-0979(1982)14971-0
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