"Spectral Theory and Mathematical Physics"
In honor of Vladimir Georgescu
Cergy-Pontoise, June 21-24, 2016.
Photo Credit: Cergy - Axe majeur,
www.cergypontoise.fr/jcms/p2_85721/fr/le-patrimoine-moderne
| Program Spyros Alexakis Kaïs Ammari Jean-Marc Bouclet Jan Derezinski Clotilde Fermanian Kammerer Christian Gérard Sylvain Golénia Dietrich Häfner Matti Lassas Mathieu Lewin Jacob Schach Moller Francis Nier Victor Nistor Benoit Pausader Main page |
Jacob Schach Moller: Local Spectral Deformation Abstract: It is well known that the usefulness of dilation analyticity is intimately connected with the role of the generator of dilation in Mourre theory for Schrodinger operators. If one expands the dilated Hamiltonian in powers of a dilation parameter, the leading order correction to the Hamiltonian is the commutator between the Hamiltonian and the dilation generator. In principle, a Mourre estimate should therefore cause the non-normal dilated Hamiltonian to form a gap in its essential spectrum, locally where a Mourre estimate is valid. This will lay bare embedded eigenvalues and enable an application of Kato's analytic perturbation theory. In this talk we pursue this scheme in a an abstract setting, and apply it to two-body dispersive system where we show that the non-threshold part of the embedded energy-momentum point spectrum form a semi-analytic subset of the complement of the threshold set in energy-momentum space. The talk is based on joint work with Matthias Engelman and Morten Grud Rasmussen. |
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