Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

   
 
 

 

Reflection symmetries and absence of eigenvalues for one-dimensional Schrödinger operators


Authors: David Damanik and Dirk Hundertmark
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1957-1962
MSC (2000): Primary 34L05, 47E05, 81Q10
DOI: https://doi.org/10.1090/S0002-9939-04-06985-0
Published electronically: February 26, 2004
MathSciNet review: 2053966
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a criterion for absence of decaying solutions for one-dimensional Schrödinger operators. As necessary input, we require infinitely many centers of local reflection symmetry and upper and lower bounds for the traces of the associated transfer matrices.


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

  • 1. D. Damanik, Gordon-type arguments in the spectral theory of one-dimensional quasicrystals, in Directions in Mathematical Quasicrystals, Eds. M. Baake and R. V. Moody, CRM Monograph Series, vol. 13, American Mathematical Society, Providence, RI, 2000, pp. 277-305. MR 2002c:81048
  • 2. D. Damanik, J.-M. Ghez, and L. Raymond, A palindromic half-line criterion for absence of eigenvalues and applications to substitution Hamiltonians, Ann. Henri Poincaré 2 (2001), 927-939. MR 2002k:81060
  • 3. S. Jitomirskaya and B. Simon, Operators with singular continuous spectrum: III. Almost periodic Schrödinger operators, Commun. Math. Phys. 165 (1994), 201-205. MR 97a:47003
  • 4. B. Simon, Schrödinger semigroups, Bull. Amer. Math. Soc. 7 (1982), no. 3, 447-526. MR 86b:81001a

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 34L05, 47E05, 81Q10

Retrieve articles in all journals with MSC (2000): 34L05, 47E05, 81Q10


Additional Information

David Damanik
Affiliation: Department of Mathematics 253–37, California Institute of Technology, Pasadena, California 91125
Email: damanik@its.caltech.edu

Dirk Hundertmark
Affiliation: Department of Mathematics 253–37, California Institute of Technology, Pasadena, California 91125
Address at time of publication: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green St., Urbana, Illinois 61801
Email: dirkh@caltech.edu, dirk@math.uiuc.edu

DOI: https://doi.org/10.1090/S0002-9939-04-06985-0
Keywords: Schr\"odinger operators, eigenvalue problem, local reflection symmetries
Received by editor(s): July 3, 2002
Received by editor(s) in revised form: August 1, 2002
Published electronically: February 26, 2004
Additional Notes: Supported in part by NSF grant DMS-0010101
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 by the authors

American Mathematical Society