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An optimal $L^p$ bound on the Krein spectral shift function.
Probability| Speaker: | Dr. Dirk Hundertmark, California Institute of Technology |
| Location: | 693 Kerr |
| Start time: | Tue, Oct 31 2000, 3:10PM |
Description
Let $xi_{A,B}$ be the Krein spectral shift function for a pair of
operators $A,B$, with $C=A-B$ trace class. We establish the bound
egin{displaymath}
int F(abs{xi_{A,B}(lambda)}), dlambda
le
int F(abs{xi_{abs{C},0}(lambda)}), dlambda
=
sum_{j=1}^infty ig[F(j)-F(j-1)]mu_j(C),
end{displaymath}
where $F$ is any non-negative convex function on $[0,infty)$ with
$F(0)=0$ and $mu_j(C)$ are the singular values of $C$.
Specializing to $F(t)=t^p$, $pge 1$ this improves a recent bound
of Combes, Hislop, and Nakamura.