Bernstein theorems and transformations of correlation measures in statistical physics
We study the class of endomorphisms of the cone of correlation functions generated by probability measures. We consider algebraic properties of the products ((.), star) and the maps K, K-1 which establish relationships between the properties of functions on the configuration space and the properties of the corresponding operators (matrices with Boolean indices): F(gamma) -> (F) over cap (boolean OR)(gamma) = {F(alpha boolean OR beta)}alpha beta subset of gamma. For the operators (F) over cap (boolean OR)(gamma) and (F) over cap (boolean AND)(gamma), we prove conditions which ensure that these operators are positive definite; the conditions are given in terms of complete or absolute monotonicity properties of the function F(gamma).
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5-6
649-663
649-663
CONSULTANTS BUREAU/SPRINGER