AG Mathematische Physik: Evgeny Korotyaev (Changchun, China): Inverse resonance scattering on rotationally symmetric manifolds
Evgeny Korotyaev (Changchun, China)
Inverse resonance scattering on rotationally symmetric manifolds
Evgeny Korotyaev jointly with Hiroshi Isozaki
Academy for Advance interdisciplinary Studies, Northeast Normal University
We discuss inverse resonance scattering for the
Laplacian on a
rotationally symmetric manifold M = (0,\infty) x Y whose
rotation radius is constant outside some compact interval.
Here Y is a compact m-dimensional Riemannian manifold.
The Laplacian on M is unitarily equivalent to a direct sum of
one-dimensional Schrodinger operators with compactly supported
potentials on the half-line. We prove
1) Asymptotics of counting function of resonances at large radius.
2) The rotation radius is uniquely determined by its
eigenvalues and resonances.
3) There exists an algorithm to recover the rotation radius
from its eigenvalues and resonances.
The proof is based on some non-linear real analytic isomorphism
between two Hilbert spaces.