- 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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