Perturbations of discrete lattices and almost periodic sets

dc.contributor.authorFavorov, S.
dc.contributor.authorKolbasina, Y.
dc.date.accessioned2019-06-15T16:12:52Z
dc.date.available2019-06-15T16:12:52Z
dc.date.issued2010
dc.description.abstractA 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.uk_UA
dc.identifier.citationPerturbations 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.uk_UA
dc.identifier.issn1726-3255
dc.identifier.other2000 Mathematics Subject Classification:11K70; 52C07, 52C23.
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/154502
dc.language.isoenuk_UA
dc.publisherІнститут прикладної математики і механіки НАН Україниuk_UA
dc.relation.ispartofAlgebra and Discrete Mathematics
dc.statuspublished earlieruk_UA
dc.titlePerturbations of discrete lattices and almost periodic setsuk_UA
dc.typeArticleuk_UA

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