Proceedings of the American Mathematical Society

Author(s): Christian Remling
Journal: Proc. Amer. Math. Soc. 128 (2000), 161-171.
MSC (1991): Primary 34L40, 81Q10
Posted: June 24, 1999
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Abstract: We show that the solutions of the one-dimensional Schrödinger equation

with potential $V(x)=O(x^{-\alpha})$ satisfy the WKB asymptotic formulae off a set of energies

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.

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

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

DOI: 10.1090/S0002-9939-99-05110-2
PII: S 0002-9939(99)05110-2
Received by editor(s): March 10, 1998
Posted: June 24, 1999
Communicated by: Christopher D. Sogge
Copyright of article: Copyright 1999, American Mathematical Society

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