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Spectral Shift Function in the Large Coupling Constant Limit

✍ Scribed by O Safronov

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
148 KB
Volume
182
Category
Article
ISSN
0022-1236

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✦ Synopsis

Given two selfadjoint operators H 0 and V=V + &V & , we study the spectrum of the operator H(:)=H 0 +:V, :>0. We consider the quantity !(*, H(:), H 0 ), * # R, which coincides with Krein's spectral shift function of the pair H(:), H 0 if V is of trace class and study its asymptotic behavior as : Ä . Applications to differential operators are given. 2001 Academic Press !(*, :)=tr(E H 0 (& , *)&E H(:) (& , *)).

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