A Characteristic decay semigroup for the resonances of trace class perturbations with analyticity conditions of semibounded hamiltonians
- To asymptotic complete scattering systems {M(+) + V, M(+)} on H(+) := L(2)(R(+), K, d lambda), where M(+) is the multiplication operator on H(+) and V is a trace class operator with analyticity conditions, a decay semigroup is associated such that the spectrum of the generator of this semigroup coincides with the set of all resonances (poles of the analytic continuation of the scattering matrix into the lower half plane across the positive half line), i.e. the decay semigroup yields a "time-dependent" characterization of the resonances. As a counterpart a "spectral characterization" is mentioned which is due to the "eigenvalue-like" properties of resonances.
Author details: | Hellmut Baumgärtel |
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DOI: | https://doi.org/10.1007/s10773-010-0533-9 |
ISSN: | 0020-7748 |
Title of parent work (English): | International journal of theoretical physic |
Publisher: | Springer |
Place of publishing: | New York |
Publication type: | Article |
Language: | English |
Year of first publication: | 2011 |
Publication year: | 2011 |
Release date: | 2017/03/26 |
Tag: | Decay semigroups; Lax-Phillips theory; Resonances; Scattering theory |
Volume: | 50 |
Issue: | 7 |
Number of pages: | 7 |
First page: | 2002 |
Last Page: | 2008 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Peer review: | Referiert |