Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bounds on embedded singular spectrum
for one-dimensional Schrödinger operators


Author: Christian Remling
Journal: Proc. Amer. Math. Soc. 128 (2000), 161-171
MSC (1991): Primary 34L40, 81Q10
Published electronically: June 24, 1999
MathSciNet review: 1637420
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that the solutions of the one-dimensional Schrödinger equation $-y''+Vy=Ey$ with potential $V(x)=O(x^{-\alpha})$ satisfy the WKB asymptotic formulae off a set of energies $E$ of Hausdorff dimension $\le 2(1-\alpha)$. This result gives restrictions on the structure of possible embedded singular spectrum. The proof relies on new norm estimates for the integral transform associated with the WKB method.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34L40, 81Q10

Retrieve articles in all journals with MSC (1991): 34L40, 81Q10


Additional Information

Christian Remling
Affiliation: Universität Osnabrück, Fachbereich Mathematik/Informatik, 49069 Osnabrück, Germany
Email: cremling@mathematik.uni-osnabrueck.de

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05110-2
PII: S 0002-9939(99)05110-2
Received by editor(s): March 10, 1998
Published electronically: June 24, 1999
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1999 American Mathematical Society