02-298 V. Bruneau, V. Petkov

Eigenvalues of the reference operator and semiclassical resonances (58K, LateX 2e) Jul 9, 02

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Abstract. We prove that the estimate of the number of the eigenvalues in intervals $[\lambda - \delta, \lambda + \delta],\:\:\: 0 < \frac{h}{C} \leq \delta \leq C$, of the reference operator $L^{\#}(h)$ related to a self-adjoint operator $L(h)$ is equivalent to the estimate of the integral over $[\lambda - \delta, \lambda + \delta]$ of the sum of harmonic measures associated to the resonances of $L(h)$ lying in a complex neighborhood $\Omega$ of $\lambda > 0$ and the number of the positive eigenvalues of $L(h)$ in $[\lambda - \delta, \lambda + \delta]$. We apply this result to obtain a Breit-Wigner approximation of the derivative of the spectral shift function near critical energy levels.

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