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An Operator-Theoretic Proof of an Estimate on the Transfer Operator

✍ Scribed by Stéphane Descombes; Boun Oumar Dia

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
255 KB
Volume
165
Category
Article
ISSN
0022-1236

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✦ Synopsis

Let \ be a nonnegative number; denote W1Â\X as the smallest integer which is larger than 1Â. Let k=max(2 W1Â\X, 4), and let V be a positive potential on R N of class C k such that for all multi-index :

as t decreases to zero. Our techniques rely on estimates on commutators. 1999 Academic Press Soit \ un re el strictement positif, notons W1Â\X le plus petit entier supe rieur ou e gal aÁ 1Â. Soit V un potentiel positif sur R N de classe C k tel que pour tout multiindice : satisfaisant |:| k on ait | : V(x)| C : (1+V(x)) (1&\ |:|)+ . Nous prouvons que

&e &tV e 2t2 e &tV &e 2t(&V+2) & L(L 2 ) =O(t 1+2 inf( , 1Â2) ) quand t decroi^t vers ze ro. Nos techniques utilisent des estimations sur des commutateurs.

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