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Trace estimates and invariance of the essential spectrum

G. Barbatis
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Abstract

We provide sufficient conditions under which the difference of the resolvents of two higher-order operators acting in $\R^N$ belongs to trace classes $\cC^p$. We provide explicit estimates on the norm of the resolvent difference in terms of $L^p$ norms of the difference of the coefficients. Such inequalities are useful in estimating the effect of localized perturbations of the coefficients.

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G. Barbatis. 2006-01-18. Trace estimates and invariance of the essential spectrum. https://arxiv.org/abs/math/0601435

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