 03220 Mouez Dimassi and Vesselin Petkov
 Spectral shift function and resonances for non semibounded and Stark hamiltonians
(440K, postscript)
May 13, 03

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We generalize for non semibounded and Stark hamiltonians the results of BruneauPetkov proving
a representation of the derivative of the spectral shift function $\xi(\lambda, h)$ related to the semiclassical resonances. For Stark hamiltonians
$P_2(h) = h^2 \Delta + \beta x_1 + V(x), \beta > 0$ we obtain a local trace formula and we establish an upper bound for the number of
the resonances in a compact domain $\Omega \subset C_{}$.
For potentials $V \in C_0^{\infty}(R^n)$ with ${\rm supp}_{x_1} V \subset [R_0, + \infty[$, we obtain a Weyltype asymptotics of $\xi(\lambda, h)$ and we
establish the existence of resonances in every hindependent complex neighborhood of $E_0$ if $E_0$
is an analytic singularity of a suitable measure related to $V$.
 Files:
03220.src(
03220.keywords ,
ssfgen21.ps )