 9540 Eckmann J.P., Pillet C.A.
 Scattering Phases and Density of States for Exterior Domains
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Feb 4, 95

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Abstract. For a bounded open domain $\Omega\in \real^2$ with
connected complement
and piecewise smooth boundary, we consider the Dirichlet
Laplacian $\DO$ on $\Omega$ and the Smatrix on the complement $\Omega^c$.
Using the restriction $A_E$ of $(\DeltaE)^{1}$ to the boundary of $\Omega
$, we establish that $A_{E_0}^{1/2}A_EA_{E_0}^{1/2}1$ is trace class
when $E_0$ is
negative and give bounds on the energy dependence of this difference.
This allows for precise bounds on the total scattering phase,
the definition of a $\zeta$function, and a Krein spectral formula, which
improve similar results found in the literature.
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