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Reflection symmetries and absence of eigenvalues for one-dimensional Schrödinger operators
Author(s):
David
Damanik;
Dirk
Hundertmark
Journal:
Proc. Amer. Math. Soc.
132
(2004),
1957-1962.
MSC (2000):
Primary 34L05, 47E05, 81Q10
Posted:
February 26, 2004
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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:
-
- 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
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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:
10.1090/S0002-9939-04-06985-0
PII:
S 0002-9939(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
Posted:
February 26, 2004
Additional Notes:
Supported in part by NSF grant DMS-0010101
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2004,
by the authors
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