Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 408

Spectral shift function in the large coupling constant limit

Oleg Safronov

Given two selfadjoint operators $H_0$ and $V=V_+-V_-$, we study the motion of the spectrum of the operator $H(alpha)=H_0+alpha V$ as $alpha$ increases. Let $lambda$ be a real number. We consider the quantity $xi(lambda,H(alpha),H_0)$ defined as a generalization of Krein's spectral shift function of the pair $H(alpha), H_0$. We study the asymptotic behavior of $xi(lambda,H(alpha),H_0)$ as $alpha o infty.$ Applications to differential operators are given.

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