Pushnitski, A. B.
Integral estimates for the spectral shift function 
(80K, LATeX 2e)

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.