T. Kriecherbauer et C. Remling, Finite gap potentials and WKB asymptotics for one-dimensional Schrodinger operators, COMM MATH P, 223(2), 2001, pp. 409-435
Consider the Schrodinger operator H = -d(2)/dx(2) + V(X) with power-decayin
g potential V(x) = O(x(-alpha)). We prove that a previously obtained dimens
ional bound on exceptional sets of the WKB method is sharp in its whole ran
ge of validity. The construction relies on pointwise bounds:on finite gap p
otentials. These bounds are obtained by an analysis of the Jacobi inversion
problem on hyperelliptic Riemann surfaces.