99-332 Oleg Safronov
Spectral shift function in the large coupling constant limit (115K, Postscript) Sep 10, 99
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Abstract. 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 $\alpha\to \infty.$ Applications to differential operators are given.

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