Bernstein theorems and transformations of correlation measures in statistical physicsстатья
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Дата последнего поиска статьи во внешних источниках: 2 апреля 2015 г.
Аннотация:We study the class of endomorphisms of the cone of correlation functions generated by probability measures. We consider algebraic properties of the products (⋅,⋆) 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(γ)→Fˆ∪(γ)={F(α∪β)}α,β⊂γ. For the operators Fˆ∪(γ) and Fˆ∩(γ), 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(γ)