Finite gap potentials and WKB asymptotics for one-dimensional Schrodinger operators

Autor(en): Kriecherbauer, T
Remling, C
Stichwörter: ABSOLUTELY CONTINUOUS-SPECTRUM; DECAYING POTENTIALS; Physics; Physics, Mathematical
Erscheinungsdatum: 2001
Herausgeber: SPRINGER-VERLAG
Journal: COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volumen: 223
Ausgabe: 2
Startseite: 409
Seitenende: 435
Zusammenfassung: 
Consider the Schrodinger operator H = -d(2)/dx(2) V(X) with power-decaying potential V(x) = O(x(-alpha)). We prove that a previously obtained dimensional bound on exceptional sets of the WKB method is sharp in its whole range of validity. The construction relies on pointwise bounds:on finite gap potentials. These bounds are obtained by an analysis of the Jacobi inversion problem on hyperelliptic Riemann surfaces.
ISSN: 00103616
DOI: 10.1007/s002200100550

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