An Estimate of the Kac Transfer Operator
LetVbe a positive potential classC4on Rnsuch that its derivatives of order 2 to 4 are bounded. We prove that‖exp(−tV)exp(2tΔ)exp(−tV)−exp(−2t(−Δ+V))‖L(L2)=O(t2)asttends to zero. Our assumptions are more general than those of Helffer [2], and our techniques rely on holomorphic semigroups and estimate...
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| Published in | Journal of functional analysis Vol. 145; no. 1; pp. 108 - 135 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.04.1997
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| Online Access | Get full text |
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| Summary: | LetVbe a positive potential classC4on Rnsuch that its derivatives of order 2 to 4 are bounded. We prove that‖exp(−tV)exp(2tΔ)exp(−tV)−exp(−2t(−Δ+V))‖L(L2)=O(t2)asttends to zero. Our assumptions are more general than those of Helffer [2], and our techniques rely on holomorphic semigroups and estimates on commutators.
SoitVun potentiel positif de classeC4sur Rn, tel que ses dérivées d'ordre 2 à 4 soient bornées. Nous prouvons que‖exp(−tV)exp(2tΔ)exp(−tV)−exp(−2t(−Δ+V))‖L(L2)=O(t2)quandttend vers 0. Nos hypothèses sont plus générales que celles de Helffer [2], et nous utilisons des techniques de semi-groupes holomorphes et des estimations sur des commutateurs. |
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| ISSN: | 0022-1236 1096-0783 |
| DOI: | 10.1006/jfan.1996.3024 |