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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Lugansk National Taras Shevchenko University
2018
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oai:ojs.admjournal.luguniv.edu.ua:article-6302018-04-04T09:11:25Z Perturbations of discrete lattices and almost periodic sets Favorov, Sergey Kolbasina, Yevgeniia perturbation of discrete lattice, almost periodic discrete set, signed discrete set, quasicrystals 11K70; 52C07, 52C23 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. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/630 Algebra and Discrete Mathematics; Vol 9, No 2 (2010) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/630/164 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-04-04T09:11:25Z |
| collection |
OJS |
| language |
English |
| topic |
perturbation of discrete lattice almost periodic discrete set signed discrete set quasicrystals 11K70; 52C07 52C23 |
| spellingShingle |
perturbation of discrete lattice almost periodic discrete set signed discrete set quasicrystals 11K70; 52C07 52C23 Favorov, Sergey Kolbasina, Yevgeniia Perturbations of discrete lattices and almost periodic sets |
| topic_facet |
perturbation of discrete lattice almost periodic discrete set signed discrete set quasicrystals 11K70; 52C07 52C23 |
| format |
Article |
| author |
Favorov, Sergey Kolbasina, Yevgeniia |
| author_facet |
Favorov, Sergey Kolbasina, Yevgeniia |
| author_sort |
Favorov, Sergey |
| title |
Perturbations of discrete lattices and almost periodic sets |
| title_short |
Perturbations of discrete lattices and almost periodic sets |
| title_full |
Perturbations of discrete lattices and almost periodic sets |
| title_fullStr |
Perturbations of discrete lattices and almost periodic sets |
| title_full_unstemmed |
Perturbations of discrete lattices and almost periodic sets |
| title_sort |
perturbations of discrete lattices and almost periodic sets |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/630 |
| work_keys_str_mv |
AT favorovsergey perturbationsofdiscretelatticesandalmostperiodicsets AT kolbasinayevgeniia perturbationsofdiscretelatticesandalmostperiodicsets |
| first_indexed |
2025-07-17T10:32:45Z |
| last_indexed |
2025-07-17T10:32:45Z |
| _version_ |
1837889870081556480 |