Bernstein theorems and transformations of correlation measures in statistical physics |
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| Authors: | Yu. G. Kondratiev A. M. Chebotarev |
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| Affiliation: | (1) M. V. Lomonosov Moscow State University, Russia;(2) Bielefeld University, Bielefeld, Germany |
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| Abstract: | 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) → F?(γ) = {F(α?β)}α,β?γ. For the operators F?(γ) and F?(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). |
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| Keywords: | Lenard theorem Hibbs measure correlation functions complete positivity Hausdorff space locally finite measure K-transform |
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