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Asymptotic expansion in time of the Schrödinger group on conical manifolds. (English) Zbl 1118.35022
Ann. Inst. Fourier 56, No. 6, 1903-1945 (2006); Corrigendum 57, No. 6, 2081-2082 (2007).
Author’s abstract: For the Schrödinger operator \(P\) on Riemannian manifolds with conical end, we study the contribution of zero energy resonant states to the singularity of the resolvent of \(P\) near zero. Long-time expansion of the Schrödinger group \(U(t)= e^{-itP}\) is obtained under a non-trapping condition at high energies.
In the corrigendum the authors correct an error in the normalizing constant of resonant states.

MSC:
35P25 Scattering theory for PDEs
47A40 Scattering theory of linear operators
58J37 Perturbations of PDEs on manifolds; asymptotics
81U10 \(n\)-body potential quantum scattering theory
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