메뉴 건너뛰기




Volumn 154, Issue 1, 2001, Pages 155-203

Hölder continuity of the integrated density of states for quasi-periodic Schrödinger equations and averages of shifts of subharmonic functions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035535652     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/3062114     Document Type: Article
Times cited : (206)

References (39)
  • 1
    • 24244444170 scopus 로고
    • Absence of diffusion in certain random lattices
    • P. ANDERSON, Absence of diffusion in certain random lattices, Phys. Rev. 109 (1958), 1492-1501.
    • (1958) Phys. Rev. , vol.109 , pp. 1492-1501
    • Anderson, P.1
  • 2
    • 21344491724 scopus 로고
    • Localization at large disorder and at extreme energies: An elementary derivation
    • M. AIZENMAN and S. MOLCHANOV, Localization at large disorder and at extreme energies: an elementary derivation, Comm. Math. Phys. 157 (1993), 245-278.
    • (1993) Comm. Math. Phys. , vol.157 , pp. 245-278
    • Aizenman, M.1    Molchanov, S.2
  • 3
    • 84972566320 scopus 로고
    • Almost periodic Schrödinger operators II. The integrated density of states
    • J. AVRON and B. SIMON, Almost periodic Schrödinger operators II. The integrated density of states, Duke Math. J. 50 (1983), 369-391.
    • (1983) Duke Math. J. , vol.50 , pp. 369-391
    • Avron, J.1    Simon, B.2
  • 4
    • 0001539982 scopus 로고
    • On the measure of the spectrum for the almost Mathieu operator
    • Erratum, ibid. 139 (1991), 215
    • J. AVRON, P. VAN MOUCHE, and B. SIMON, On the measure of the spectrum for the almost Mathieu operator, Comm. Math. Phys. 132 (1990), 103-118; Erratum, ibid. 139 (1991), 215.
    • (1990) Comm. Math. Phys. , vol.132 , pp. 103-118
    • Avron, J.1    Van Mouche, P.2    Simon, B.3
  • 5
    • 0034310141 scopus 로고    scopus 로고
    • On nonperturbative localization with quasi-periodic potential
    • J. BOURGAIN and M. GOLDSTEIN, On nonperturbative localization with quasi-periodic potential, Ann. of Math. 152 (2000), 835-879.
    • (2000) Ann. of Math. , vol.152 , pp. 835-879
    • Bourgain, J.1    Goldstein, M.2
  • 6
    • 0002730299 scopus 로고
    • A supersymmetric transfer matrix and differentiability of the density of states in the one-dimensional Anderson model
    • M. CAMPANINO and A. KLEIN, A supersymmetric transfer matrix and differentiability of the density of states in the one-dimensional Anderson model, Comm. Math. Phys. 104 (1986), 227-241.
    • (1986) Comm. Math. Phys. , vol.104 , pp. 227-241
    • Campanino, M.1    Klein, A.2
  • 8
    • 0021376497 scopus 로고
    • Analyticity of the density of states and replica method for random Schrödinger operators on a lattice
    • F. CONSTANTINESCU, J. FRÖHLICH, and T. SPENCER, Analyticity of the density of states and replica method for random Schrödinger operators on a lattice, J. Statist. Phys. 34 (1984), 571-596.
    • (1984) J. Statist. Phys. , vol.34 , pp. 571-596
    • Constantinescu, F.1    Fröhlich, J.2    Spencer, T.3
  • 10
    • 0001055893 scopus 로고
    • The one-dimensional Schrödinger equation with quasiperiodic potential
    • E. I. DINABURG and YA. G. SINAI, The one-dimensional Schrödinger equation with quasiperiodic potential, Funkt. Anal. i. Prilozhen 9 (1975), 8-21; English transl. Funct Anal. Appl. 9 (1975), 279-289.
    • (1975) Funkt. Anal. i. Prilozhen , vol.9 , pp. 8-21
    • Dinaburg, E.I.1    Sinai, Ya.G.2
  • 11
    • 34250407352 scopus 로고
    • E. I. DINABURG and YA. G. SINAI, The one-dimensional Schrödinger equation with quasiperiodic potential, Funkt. Anal. i. Prilozhen 9 (1975), 8-21; English transl. Funct Anal. Appl. 9 (1975), 279-289.
    • (1975) Funct Anal. Appl. , vol.9 , pp. 279-289
  • 13
    • 0001401431 scopus 로고
    • Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation
    • H. ELIASSON, Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation, Comm. Math. Phys. 146 (1992), 447-482.
    • (1992) Comm. Math. Phys. , vol.146 , pp. 447-482
    • Eliasson, H.1
  • 15
    • 0002119217 scopus 로고
    • Constructive proof of localization in the Anderson tight binding model
    • J. FRÖHLICH, F. MARTINELLI, E. SCOPPOLA, and T. SPENCER, Constructive proof of localization in the Anderson tight binding model, Comm. Math. Phys. 101 (1985), 21-46.
    • (1985) Comm. Math. Phys. , vol.101 , pp. 21-46
    • Fröhlich, J.1    Martinelli, F.2    Scoppola, E.3    Spencer, T.4
  • 16
    • 0000284780 scopus 로고
    • Absence of diffusion in the Anderson tight binding model for large disorder or low energy
    • J. FRÖHLICH and T. SPENCER, Absence of diffusion in the Anderson tight binding model for large disorder or low energy, Comm. Math. Phys. 88 (1983), 151-184.
    • (1983) Comm. Math. Phys. , vol.88 , pp. 151-184
    • Fröhlich, J.1    Spencer, T.2
  • 17
    • 0002835666 scopus 로고
    • A rigorous approach to Anderson localization
    • _, A rigorous approach to Anderson localization, Phys. Rep. 103 (1984), 9-25.
    • (1984) Phys. Rep. , vol.103 , pp. 9-25
  • 18
    • 0002234361 scopus 로고
    • Localization for a class of one-dimensional quasi-periodic Schrödinger operators
    • J. FRÖHLICH, T. SPENCER, and P. WITTWER, Localization for a class of one-dimensional quasi-periodic Schrödinger operators, Comm. Math. Phys. 132 (1990), 5-25.
    • (1990) Comm. Math. Phys. , vol.132 , pp. 5-25
    • Fröhlich, J.1    Spencer, T.2    Wittwer, P.3
  • 19
    • 84968508586 scopus 로고
    • Noncommuting random products
    • H. FÜRSTENBERG, Noncommuting random products, Trans. A.M.S. 108 (1963), 377-428.
    • (1963) Trans. A.M.S. , vol.108 , pp. 377-428
    • Fürstenberg, H.1
  • 20
    • 34250283162 scopus 로고
    • A pure point spectrum of the stochastic one-dimensional Schrödinger equation
    • I. YA. GOLDSHEID, S. A. MOLCHANOV, and L. PASTUR, A pure point spectrum of the stochastic one-dimensional Schrödinger equation, Funkt. Anal. Appl. 11 (1977), 1-10.
    • (1977) Funkt. Anal. Appl. , vol.11 , pp. 1-10
    • Goldsheid, I.Ya.1    Molchanov, S.A.2    Pastur, L.3
  • 21
    • 0002638383 scopus 로고    scopus 로고
    • Duality and singular continuous spectrum in the almost Mathieu equation
    • A. GORDON, S. JITOMIRSKAYA, Y. LAST, and B. SIMON, Duality and singular continuous spectrum in the almost Mathieu equation, Acta Math. 178 (1997), 169-183.
    • (1997) Acta Math. , vol.178 , pp. 169-183
    • Gordon, A.1    Jitomirskaya, S.2    Last, Y.3    Simon, B.4
  • 22
    • 28244490244 scopus 로고
    • Single band motion of conduction electrons in a uniform magnetic field
    • P. G. HARPER, Single band motion of conduction electrons in a uniform magnetic field. Proc. Phys. Soc. London A68 (1955), 874-892.
    • (1955) Proc. Phys. Soc. London , vol.A68 , pp. 874-892
    • Harper, P.G.1
  • 23
    • 51249181642 scopus 로고
    • Une méthode pour minorer les exposants de Lyapunov et quelques exemples montrant le charactère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2
    • M. HERMAN, Une méthode pour minorer les exposants de Lyapunov et quelques exemples montrant le charactère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2, Comment. Math. Helv. 58 (1983), 453-502.
    • (1983) Comment. Math. Helv. , vol.58 , pp. 453-502
    • Herman, M.1
  • 24
    • 0033235963 scopus 로고    scopus 로고
    • Metal-insulator transition for the almost Mathieu operator
    • S. JITOMIRSKAYA, Metal-insulator transition for the almost Mathieu operator, Ann. of Math. 150 (1999), 1159-1175.
    • (1999) Ann. of Math. , vol.150 , pp. 1159-1175
    • Jitomirskaya, S.1
  • 25
    • 0003918564 scopus 로고
    • The Univ. of Chicago Press, Chicago, IL
    • A. YA. KHINCHIN, Continued Fractions, The Univ. of Chicago Press, Chicago, IL, 1964.
    • (1964) Continued Fractions
    • Khinchin, A.Ya.1
  • 27
    • 33846873343 scopus 로고
    • A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants
    • Y. LAST, A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants, Comm. Math. Phys. 151 (1993), 183-192.
    • (1993) Comm. Math. Phys. , vol.151 , pp. 183-192
    • Last, Y.1
  • 28
    • 33847667155 scopus 로고
    • Zero measure spectrum for the almost Mathieu operator
    • _, Zero measure spectrum for the almost Mathieu operator, Comm. Math. Phys. 164 (1994), 421-432.
    • (1994) Comm. Math. Phys. , vol.164 , pp. 421-432
  • 30
    • 0000543733 scopus 로고
    • A multiplicative ergodic theorem: Characteristic Lyapunov, exponents of dynamical systems
    • V. OSELEDEC, A multiplicative ergodic theorem: Characteristic Lyapunov, exponents of dynamical systems, Trudy Mosc. Mat. Obzi. 19 (1968), 197-231.
    • (1968) Trudy Mosc. Mat. Obzi. , vol.19 , pp. 197-231
    • Oseledec, V.1
  • 31
    • 0033147912 scopus 로고    scopus 로고
    • On the growth and stability of real-analytic functions
    • D. H. PHONG, E. M. STEIN, and J. A. STURM, On the growth and stability of real-analytic functions, Amer. J. Math. 121 (1999), 519-554.
    • (1999) Amer. J. Math. , vol.121 , pp. 519-554
    • Phong, D.H.1    Stein, E.M.2    Sturm, J.A.3
  • 32
    • 0000695627 scopus 로고
    • On the behavior of the Schrödinger equation
    • I. SHNOL, On the behavior of the Schrödinger equation, Mat. Sb. 42, (1957), 273-286.
    • (1957) Mat. Sb. , vol.42 , pp. 273-286
    • Shnol, I.1
  • 33
    • 0000247774 scopus 로고
    • Spectrum and continuum eigenfunctions of Schrödinger operators
    • B. SIMON, Spectrum and continuum eigenfunctions of Schrödinger operators, J. Funct. Anal. 42 (1981), 347-355.
    • (1981) J. Funct. Anal. , vol.42 , pp. 347-355
    • Simon, B.1
  • 34
    • 0002809655 scopus 로고
    • Harmonic analysis on SL(2, ℝ) and smoothness of the density of states in the one-dimensional Anderson model
    • B. SIMON and M. TAYLOR, Harmonic analysis on SL(2, ℝ) and smoothness of the density of states in the one-dimensional Anderson model, Comm. Math. Phys. 101 (1985), 1-19.
    • (1985) Comm. Math. Phys. , vol.101 , pp. 1-19
    • Simon, B.1    Taylor, M.2
  • 35
    • 0000763917 scopus 로고
    • Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential
    • YA. G. SINAI, Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential, J. Statist. Phys. 46 (1987), 861-909.
    • (1987) J. Statist. Phys. , vol.46 , pp. 861-909
    • Sinai, Ya.G.1
  • 36
    • 0001305291 scopus 로고
    • Positive Lyapunov exponents for Schrödinger operators with quasi-periodic potentials
    • E. SORETS and T. SPENCER, Positive Lyapunov exponents for Schrödinger operators with quasi-periodic potentials, Comm. Math. Phys. 142 (1991), 543-566.
    • (1991) Comm. Math. Phys. , vol.142 , pp. 543-566
    • Sorets, E.1    Spencer, T.2
  • 38
    • 0000813881 scopus 로고
    • Scaling for the discrete Mathieu equation
    • D. THOULESS, Scaling for the discrete Mathieu equation, Comm. Math. Phys. 127 (1990), 187-193.
    • (1990) Comm. Math. Phys. , vol.127 , pp. 187-193
    • Thouless, D.1
  • 39
    • 0002037112 scopus 로고
    • Bounds on the density of states in disordered systems
    • F. WEGNER, Bounds on the density of states in disordered systems, Z. Phys. D B44 (1981), 9-15.
    • (1981) Z. Phys. B , vol.B44 , pp. 9-15
    • Wegner, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.