 99195 Johnsen, J.
 ON THE SPECTRAL PROPERTIES OF WITTENLAPLACIANS, THEIR RANGE PROJECTIONS AND
BRASCAMPLIEB'S INEQUALITY
(508K, Post Script)
May 26, 99

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Abstract. A study is made of a recent integral identity of B.~Helffer and
J.~Sj{\"o}strand, which for a not yet fully determined class of probability
measures yields a formula for the covariance of two functions (of
a stochastic variable); in comparison with the
BrascampLieb inequality, this formula is a more flexible and in some contexts
stronger means for the analysis of correlation asymptotics in statistical
mechanics. Using a fine version of the Closed Range Theorem, the identity's
validity is shown to be equivalent to some explicitly given
spectral properties of WittenLaplacians on Euclidean space, and
the formula is moreover deduced from the obtained abstract expression
for the range projection. As a corollary, a generalised version of
BrascampLieb's inequality is obtained. For a certain class of
measures occuring in statistical mechanics, explicit criteria for the
WittenLaplacians are found from the PerssonAgmon formula, from
compactness of embeddings and from the
Weyl calculus, which give results for closed range, strict positivity,
essential selfadjointness and domain characterisations.
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