 00403 Oleg Safronov
 The discrete spectrum of selfadjoint operators
under perturbations of variable sign
(256K, Postscript)
Oct 13, 00

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Abstract. Given two selfadjoint operators $A$ and $V=V_+V_$,
we study the motion of the eigenvalues of the operator
$A(t)=AtV$ as $t$ increases. Let $\alpha>0$ and let
$\lambda$ be a regular point for $A$. We consider
the quantity $N(\lambda,A,W_+,W_,\alpha)$ defined as
the difference between the number of the eigenvalues of
$A(t)$ that pass the point $\lambda$ from right to
left and the number of the eigenvalues
passing $\lambda$ from left to right
as $t$ increases from $0$ to $\alpha.$
We study the asymptotic behavior of $N(\lambda,A,W_+,W_,\alpha)$
as $\alpha\to \infty.$
Applications to Schr\"odinger and Dirac operators are given.
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