Bernstein theorems and transformations of correlation measures in statistical physics |
| |
| Authors: | Yu G Kondratiev A M Chebotarev |
| |
| Institution: | (1) M. V. Lomonosov Moscow State University, Russia;(2) Bielefeld University, Bielefeld, Germany |
| |
| 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). |
| |
| Keywords: | Lenard theorem Hibbs measure correlation functions complete positivity Hausdorff space locally finite measure K-transform |
| 本文献已被 SpringerLink 等数据库收录！ |
