SEMINAIRE MERCREDI 8 JUIN 2005
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Evgeny Korotyaev
Math Dept, Univ Berlin

Title: Inverse problem for harmonic oscillator perturbed by potential on the
half-line, characterization

Abstract: Consider the harmonic oscillator perturbed by a potential on the
half-line. We solved the inverse problem (including characterization)
for the mapping: potential - spectral data, where the spectral data =
the corresponding eigenvalues plus the norming constants.
The proof is based on nonlinear functional analysis combined with
sharp asymptotics of spectral data in the high energy limit for
complex potentials. We use ideas from the analysis of the inverse
problem for the case of the real line [1]. This is the joint paper
with D. Chelkak.

[1] D. Chelkak, P. Kargaev, E. Korotyaev: The inverse problem for the
harmonic oscillator perturbed by a potential. Characterization,
Commun. Math. Phys. 249 (2004), no 1, 133 - 196