# Estimates for the spectral shift function of the polyharmonic operator

@article{Pushnitski1999EstimatesFT, title={Estimates for the spectral shift function of the polyharmonic operator}, author={Alexander Pushnitski}, journal={Journal of Mathematical Physics}, year={1999}, volume={40}, pages={5578-5592} }

The Lifshits–Krein spectral shift function is considered for the pair of operators H0=(−Δ)l, l>0 and H=H0+V in L2(Rd), d⩾1; here V is a multiplication operator. The estimates for this spectral shift function ξ(λ;H,H0) are obtained in terms of the spectral parameter λ>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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