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This article is cited in 5 scientific papers (total in 5 papers) On the analogues of Szegő's theorem for ergodic operators W. Kirsсha, L. Pasturb† a FernUniversität in Hagen b B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar'kov Abstract: Szegő's theorem on the asymptotic behaviour of the determinants of large Toeplitz matrices is generalized to the class of ergodic operators. The generalization is formulated in terms of a triple consisting of an ergodic operator and two functions, the symbol and the test function. It is shown that in the case of the one-dimensional discrete Schrödinger operator with random ergodic or quasiperiodic potential and various choices of the symbol and the test function this generalization leads to asymptotic formulae which have no analogues in the situation of Toeplitz operators. Bibliography: 22 titles. Keywords: Szegő's theorem, random operators, limit theorems. † Author to whom correspondence should be addressed DOI: https://doi.org/10.4213/sm8318   Full text:
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English version: Sbornik: Mathematics, 2015, 206:1, Bibliographic databases:      
UDC: 517.983.28+519.214+519.216.75 MSC: Primary 47B99; Secondary 35J10, 47B80 Received: 24.12.2013 and 23.07.2014 Citation: W. Kirsсh, L. Pastur, “On the analogues of Szegő's theorem for ergodic operators”, Mat. Sb., 206:1 (2015), 
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