Lemańczyk, M.; Parreau, F. On the disjointness problem for Gaussian automorphisms. (English) Zbl 0923.28007 Proc. Am. Math. Soc. 127, No. 7, 2073-2081 (1999). Let \((T_\sigma,X,{\mathcal B},\mu_\sigma)\) be a Gaussian dynamical system with (symmetric) spectral measure \(\sigma=\sigma_{f_0}\), where \(f_0\) denotes the 0-coordinate projection. The authors show that any two Gaussian dynamical systems \((T_\sigma,X,{\mathcal B},\mu_\sigma)\) and \((T_\tau,X,{\mathcal B},\mu_\tau)\) for which \(\sigma\) and \(\tau\) are concentrated on independent sets are either spectrally disjoint or have a common factor. Thus in this case, disjointness as introduced by H. Furstenberg [Math. Systems Theory 1, 1-49 (1967; Zbl 0146.28502)] is equivalent to \(\sigma\) and \(\tau\) being mutually singular. As an application of the approach used in this paper, the authors were able to construct non-rigid Gaussian automorphisms which are spectrally determined: spectral isomorphism implies measure theoretic isomorphism. Reviewer: Karma Dajani (Utrecht) Cited in 1 ReviewCited in 5 Documents MSC: 28D05 Measure-preserving transformations 43A05 Measures on groups and semigroups, etc. Keywords:Kronecker sets; Gaussian dynamical systems; disjointness; Gaussian automorphisms Citations:Zbl 0146.28502 PDFBibTeX XMLCite \textit{M. Lemańczyk} and \textit{F. Parreau}, Proc. Am. Math. Soc. 127, No. 7, 2073--2081 (1999; Zbl 0923.28007) Full Text: DOI