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On orthogonality to uniquely ergodic systems
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We solve Boshernitzan's problem of characterization (in terms of so called Furstenberg systems) of bounded sequences that are orthogonal to all uniquely ergodic systems. Some variations of Boshernitzan's problem involving characteristic classes are considered. As an application, we characterize sequences orthogonal to all uniquely ergodic systems whose (unique) invariant measure yields a discrete spectrum automorphism as those satisfying an averaged Chowla property.
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Cited by 2 Pith papers
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On some classification problems of multiplicative functions
Multiplicative Toeplitz sequences are exactly Dirichlet characters away from a finite prime set, and unique Furstenberg systems for pretentious functions coincide with rational almost periodicity.
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On systems disjoint from all minimal systems
A topological system is disjoint from every minimal system exactly when it has countably many dense minimal subsets each disjoint from it, with analogous residual-pair and distal characterizations.
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