On uniformly distributed sequences of integers and Poincaré recurrence
type: Item
instance of: scholarly article
title: On uniformly distributed sequences of integers and Poincaré recurrence
zbMATH Open document ID: 0922.11064
DOI: 10.1016/S0019-3577(97)87567-2
author: K. Appert
published in: Indagationes Mathematicae. New Series
publication date: 1999-06-01T00:00:00Z
review text: The author proves that Hartmann-uniformly distributed sequences are sequences of strong Poincaré recurrence. Theorems 1, 2 in fact follow (from equality instead of the stated inequality) already from the much more general fact, that Hartmann-uniformly distributed sequences are uniformly distributed with respect to any unitary representation (even with respect to the strong operator topology) not only for locally compact abelian groups, as considered here (or groups with only finite-dimensional irreducible representations, considering a natural generalization), see [\textit{J. Blum} and \textit{B. Eisenberg}, Proc. Am. Math. Soc. 42, 423-429 (1974; Zbl 0273.43004) and \textit{H. Rindler}, Monatsh. Math. 82, 207-235 (1976; Zbl 0361.43002), p. 209, Def. 4 and the following remark]. The explicit examples given in Theorem 4 are interesting, but most of them are well-known. For Part II see Zbl 0922.11065.
reviewed by: Harald Rindler
Mathematics Subject Classification ID: 11K06
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 1251251
zbMATH Keywords: Poincaré recurrence
zbMATH Keywords: Hartmann-uniformly distributed sequences
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1251251