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1995-1996 | 117 | 2 | 149-171
Tytuł artykułu

Ergodic theory for the one-dimensional Jacobi operator

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We determine the number and properties of the invariant measures under the projective flow defined by a family of one-dimensional Jacobi operators. We calculate the derivative of the Floquet coefficient on the absolutely continuous spectrum and deduce the existence of the non-tangential limit of Weyl m-functions in the $L^1$-topology.
Słowa kluczowe
Czasopismo
Rocznik
Tom
117
Numer
2
Strony
149-171
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-04-04
poprawiono
1995-06-19
Twórcy
  • Departamento de Matemática Aplicada a la Ingeniería, Escuela Técnica Superior de Ingenieros Industriales, Universidad de Valladolid, Paseo del Cauce S/N, E-47011 Valladolid, Spain, carnun@wmatem.eis.uva.es
autor
  • Departamento de Matemática Aplicada a la Ingeniería, Escuela Técnica Superior de Ingenieros Industriales, Universidad de Valladolid, Paseo del Cauce S/N, E-47011 Valladolid, Spain, rafoba@wmatem.eis.uva.es
Bibliografia
  • [1] P. Deift and B. Simon, Almost periodic Schrödinger operators III, Comm. Math. Phys. 90 (1983), 389-411.
  • [2] F. Delyon and B. Souillard, The rotation number for finite difference operators and its properties, ibid. 89 (1983), 415-426.
  • [3] R. Johnson, Analyticity of spectral subbundles, J. Differential Equations 35 (1980), 366-387.
  • [4] R. Johnson, Exponential dichotomy, rotation number, and linear differential equations with bounded coefficients, ibid. 61 (1986), 54-78.
  • [5] S. Kotani, Lyapunov indices determine absolutely continuous spectrum of stationary random 1-dimensional Schrödinger equations, in: Stochastic Analysis, K. Ito (ed.), North-Holland, Amsterdam, 1984, 225-248.
  • [6] 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.
  • [7] S. Novo and R. Obaya, An ergodic classification of bidimensional linear systems, preprint, University of Valladolid, 1994.
  • [8] C. Núñez and R. Obaya, Non-tangential limit of the Weyl m-functions for the ergodic Schrödinger equation, preprint, University of Valladolid, 1994.
  • [9] C. Núñez and R. Obaya, Semicontinuity of the derivative of the rotation number, C. R. Acad. Sci. Paris Sér. I 320 (1995), 1243-1248.
  • [10] R. Obaya and M. Paramio, Directional differentiability of the rotation number for the almost periodic Schrödinger equation, Duke Math. J. 66 (1992), 521-552.
  • [11] V. Oseledec, A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc. 19 (1968), 197-231.
  • [12] L. Pastur, Spectral properties of disordered systems in the one body approximation, Comm. Math. Phys. 75 (1980), 179-196.
  • [13] R. J. Sacker and G. R. Sell, A spectral theory for linear differential systems, J. Differential Equations 27 (1978), 320-358.
  • [14] B. Simon, Kotani theory for one dimensional stochastic Jacobi matrices, Comm. Math. Phys. 89 (1983), 227-234.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv117i2p149bwm
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