99-48 Alexander Pushnitski

Estimates for the spectral shift function of the polyharmonic operator (50K, Latex 2e) Feb 12, 99

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Abstract. The Lifshits--Krein spectral shift function is considered for the pair of operators $H_0=(-\bigtriangleup)^l$, $l>0$ and $H=H_0+V$ in $L_2(\R^d)$, $d\geq1$; here $V$ is a multiplication operator. The estimates for this spectral shift function $\xi(\lambda;H,H_0)$ are obtained in terms of the spectral parameter $\lambda>0$ and the integral norms of $V$. These estimates are in a good agreement with the ones predicted by the classical phase space volume considerations.

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