2019/04/18 by Hiroshi Isozaki, Isozaki, Hiroshi, Evgeny Korotyaev +1
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #Numerical methods in inverse problems #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1904.08908
openalex publication_date 2019/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss inverse resonance scattering for the Laplacian on a rotationally symmetric manifold M = (0,∞) × Y whose rotation radius is constant outside some compact interval. The Laplacian on M is unitarily equivalent to a direct sum of one-dimensional Schrödinger operators with compactly supported potentials on the half-line. We prove o Asymptotics of counting function of resonances at large radius o Inverse problem: The rotation radius is uniquely determined by its eigenvalues and resonances. Moreover, 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.