Time-dependent scattering theory for Schrödinger operators on scattering manifolds
- Autores: Kenichi Ito, Shu Nakamura
- Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 81, Nº 3, 2010, págs. 774-792
- Idioma: inglés
- DOI: 10.1112/jlms/jdq018
- Enlaces
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Resumen
We construct a time-dependent scattering theory for Schr�Nodinger operators on a manifold M with asymptotically conic structure. We use the two-space scattering theory formalism, and a reference operator on a space of the form R �~ �ÝM, where �ÝM is the boundary of M at infinity. We prove the existence and the completeness of the wave operators, and show that our scattering matrix is equivalent to the absolute scattering matrix, which is defined in terms of the asymptotic expansion of generalized eigenfunctions. Our method is functional analytic, and we use no microlocal analysis in this paper.
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