Perturbations of discrete lattices and almost periodic sets
A discrete set in the p-dimensional Euclidian space is almost periodic, if the measure with the unite masses at points of the set is almost periodic in the weak sense. We propose to construct positive almost periodic discrete sets as an almost periodic perturbation of a full rank discrete lattice....
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| Datum: | 2010 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2010
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| Schriftenreihe: | Algebra and Discrete Mathematics |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Perturbations of discrete lattices and almost periodic sets / S. Favorov, Y. Kolbasina // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 2. — С. 48–58. — Бібліогр.: 11 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | A discrete set in the p-dimensional Euclidian space is almost periodic, if the measure with the unite masses at points of the set is almost periodic in the weak sense. We propose to construct positive almost periodic discrete sets as an almost periodic perturbation of a full rank discrete lattice. Also we prove that each almost periodic discrete set on the real axes is an almost periodic perturbation of some arithmetic progression.
Next, we consider signed almost periodic discrete sets, i.e., when the signed measure with masses +1 or -1 at points of a discrete set is almost periodic. We construct a signed discrete set that is not almost periodic, while the corresponding signed measure is almost periodic in the sense of distributions. Also, we construct a signed almost periodic discrete set such that the measure with masses +1 at all points of the set is not almost periodic. |
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