Local and global spectral shift functions in R2

The energy‐dependent trace‐class time‐delay operator associated with the transit time of a scattering system through a finite space region Σ⊆R2 is used to define a local (Σ‐dependent) version of the Krein spectral shift function. If the region Σ is a disk of radius r, it is proved that as r→∞ the lo...

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Bibliographic Details
Published in:Journal of mathematical physics 1989-02, Vol.30 (2), p.420-432
Main Authors: Bollé, D., Danneels, C., Osborn, T. A.
Format: Article
Language:English
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Summary:The energy‐dependent trace‐class time‐delay operator associated with the transit time of a scattering system through a finite space region Σ⊆R2 is used to define a local (Σ‐dependent) version of the Krein spectral shift function. If the region Σ is a disk of radius r, it is proved that as r→∞ the local spectral shift function converges, for almost all energies, to the original spectral shift function of Krein. This result continues to be valid for systems exhibiting zero‐energy resonance behavior.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.528461