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Nonautonomous bounded remainder sets. (English. Russian original) Zbl 1477.11130

Russ. Math. 62, No. 12, 81-87 (2018); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2018, No. 12, 94-101 (2018).
Summary: Nonautonomous bounded remainder sets are sequences of sets that admit a uniform estimation of the remainder term in the distribution of fractional parts of a linear function. In this paper, we give a complete description of nonautonomous bounded remainder sets in the case of periodic sequences. The result is also extended to certain classes of quasiperiodic sequences of sets. Our proofs are based on obtaining explicit formulas for the remainder term by using sums of fractional parts. This method is effective, i.e., it allows us to explicitly estimate the remainder term.

MSC:

11K06 General theory of distribution modulo \(1\)
11K38 Irregularities of distribution, discrepancy
11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
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