Geodesic
Two-Sided Estimates for the Trace of the Difference of Two Semigroups
Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 3, pp. 26-32

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This paper deals with the derivation of two-sided estimates for the trace of the difference of two semigroups generated by two Schrödinger operators in $L_{2}(\mathbb{R}^{3})$ with trace class difference of the resolvents. Use is made of a purely operator-theoretic technique. The results are stated in a rather general abstract form. The sharpness of our estimates is confirmed by the fact that they imply the asymptotic behavior of the trace of the difference of the semigroups as $t\to+0$. Our considerations are substantially based on the Krein–Lifshits formula and on the Birman–Solomyak representation for the spectral shift function.
Keywords: spectral shift function, Schrödinger operator
Mots-clés : trace formula. 
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     author = {M. Sh. Birman and V. A. Sloushch},
     title = {Two-Sided {Estimates} for the {Trace} of the {Difference} of {Two} {Semigroups}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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M. Sh. Birman; V. A. Sloushch. Two-Sided Estimates for the Trace of the Difference of Two Semigroups. Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 3, pp. 26-32. http://geodesic.mathdoc.fr/item/FAA_2009_43_3_a2/