Annales Henri Poincaré

, Volume 2, Issue 5, pp 927–939

A Palindromic Half-Line Criterion for Absence of Eigenvalues and Applications to Substitution Hamiltonians

  • D. Damanik
  • J.-M. Ghez
  • L. Raymond

DOI: 10.1007/s00023-001-8599-9

Cite this article as:
Damanik, D., Ghez, JM. & Raymond, L. Ann. Henri Poincaré (2001) 2: 927. doi:10.1007/s00023-001-8599-9

Abstract.

We prove a criterion for absence of decaying solutions on the half-line for one-dimensional discrete Schrödinger operators. As necessary inputs, we require infinitely many palindromic prefixes and upper and lower bounds for the traces of associated transfer matrices. We apply this criterion to Schrödinger operators with potentials generated by substitutions.

Copyright information

© Birkhäuser Verlag Basel, 2001

Authors and Affiliations

  • D. Damanik
    • 1
  • J.-M. Ghez
    • 2
  • L. Raymond
    • 4
  1. 1.Department of Mathematics 253-37, California Institute of Technology, Pasadena, CA 01125, USA, e-mail: damanik@its.caltech.eduUS
  2. 2.Centre de Physique Théorique, UPR 7061, Luminy Case 907, F-13299 Marseille, Cedex 9, FranceFR
  3. 3.PHYMAT, Département de Mathématiques, Université de Toulon et du Var, B.P. 132, F-83957 La Garde Cedex, France, e-mail: ghez@cpt.univ-mrs.frFR
  4. 4.L2MP - UMR 6137, Service 142, Centre Universitaire de Saint-Jérôme, F-13387 Marseille Cedex 20, FranceFR
  5. 5.Université de Provence, Marseille, France, e-mail: raymond@up.univ-mrs.frFR