Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
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

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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia