Bounds on embedded singular spectrum for one-dimensional Schrodinger operators

Autor(en): Remling, C
Stichwörter: ABSOLUTELY CONTINUOUS-SPECTRUM; DECAYING POTENTIALS; Mathematics; Mathematics, Applied; PERTURBATIONS; POINT
Erscheinungsdatum: 2000
Herausgeber: AMER MATHEMATICAL SOC
Journal: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volumen: 128
Ausgabe: 1
Startseite: 161
Seitenende: 171
Zusammenfassung: 
We show that the solutions of the one-dimensional Schrodinger 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 less than or equal to 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.
ISSN: 00029939
DOI: 10.1090/S0002-9939-99-05110-2

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