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An Estimate of the Kac Transfer Operator

โœ Scribed by Boun Oumar Dia; Michelle Schatzman

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
461 KB
Volume
145
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

Let V be a positive potential class C 4 on R n such that its derivatives of order 2 to 4 are bounded. We prove that

as t tends to zero. Our assumptions are more general than those of Helffer [2], and our techniques rely on holomorphic semigroups and estimates on commutators. 1997 Academic Press Soit V un potentiel positif de classe C 4 sur R n , tel que ses de rive es d'ordre 2 aร 4 soient borne es. Nous prouvons que &exp(&tV) exp(2t2) exp(&tV)&exp(&2t(&2+V))& L(L 2 ) =O(t 2 ) quand t tend vers 0. Nos hypotheร ses sont plus ge ne rales que celles de Helffer [2], et nous utilisons des techniques de semi-groupes holomorphes et des estimations sur des commutateurs.

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