98-415 Pushnitski, A. B.
Integral estimates for the spectral shift function (80K, LATeX 2e) Jun 6, 98
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Abstract. The spectral shift function $\xi(\lambda)$ is considered for the pair of operators $H_0$, $H_0+V$, where $H_0$ is the Schr\"odinger operator with a variable Riemannian metric and an electro-magnetic field, and $V$ is the operator of multiplication by the potential $V(x)$. For integrals of the type $\int\xi(\lambda)f(\lambda)d\lambda$, where $f(\lambda)$ is a weight, the estimates in terms of the integral characteristics of the potential $V$ are obtained. These estimates are of an asymptotically ``correct'' order in $\lambda$ and $V$; they will be used in a subsequent paper in the problem of asymptotics of $\xi(\lambda)$ in the large coupling constant limit.

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