Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



Singular continuous spectrum for a class of almost periodic Jacobi matrices

Authors: Joseph Avron and Barry Simon
Journal: Bull. Amer. Math. Soc. 6 (1982), 81-85
MSC (1980): Primary 47A10, 47A25; Secondary 81Cxx
MathSciNet review: 634437
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • Serge Aubry and Gilles André, Analyticity breaking and Anderson localization in incommensurate lattices, Group theoretical methods in physics (Proc. Eighth Internat. Colloq., Kiryat Anavim, 1979) Ann. Israel Phys. Soc., vol. 3, Hilger, Bristol, 1980, pp. 133–164. MR 626837
  • Serge Aubry, The new concept of transitions by breaking of analyticity in a crystallographic model, Solitons and condensed matter physics (Proc. Sympos. Nonlinear (Soliton) Structure and Dynamics in Condensed Matter, Oxford, 1978) Springer Ser. Solid-State Sci., vol. 8, Springer, Berlin-New York, 1978, pp. 264–277. MR 522493
  • 3. J. Avron and B. Simon, Almost periodic Schrödinger operators. II. The density of states and the André-Aubry Theorem (in preparation).
  • Ju. M. Berezans′kiĭ, Expansions in eigenfunctions of selfadjoint operators, Translations of Mathematical Monographs, Vol. 17, American Mathematical Society, Providence, R.I., 1968. Translated from the Russian by R. Bolstein, J. M. Danskin, J. Rovnyak and L. Shulman. MR 0222718
  • A. Ja. Gordon, The point spectrum of the one-dimensional Schrödinger operator, Uspehi Mat. Nauk 31 (1976), no. 4(190), 257–258 (Russian). MR 0458247
  • 6. R. Johnson, The recurrent Hill’s equation, U.S.C. preprint.
  • V. I. Oseledec, A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems, Trudy Moskov. Mat. Obšč. 19 (1968), 179–210 (Russian). MR 0240280
  • 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.
  • D. B. Pearson, Singular continuous measures in scattering theory, Comm. Math. Phys. 60 (1978), no. 1, 13–36. MR 484145
  • Michael Reed and Barry Simon, Methods of modern mathematical physics. I, 2nd ed., Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1980. Functional analysis. MR 751959
  • David Ruelle, Sensitive dependence on initial condition and turbulent behavior of dynamical systems, Bifurcation theory and applications in scientific disciplines (Papers, Conf., New York, 1977) Ann. New York Acad. Sci., vol. 316, New York Acad. Sci., New York, 1979, pp. 408–416. 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.

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1980): 47A10, 47A25, 81Cxx

Retrieve articles in all journals with MSC (1980): 47A10, 47A25, 81Cxx

Additional Information