Uniqueness theorem for Fourier transformable measures on LCA groups
We show that if points of supports of two discrete ”not very thick” Fourier transformable measures on locally compact abelian (LCA) groups tend to one another at infinity and the same is true for the masses at these points, then these measures coincide. The result is valid for discrete almost period...
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| Format: | Article |
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Ivan Franko National University of Lviv
2020-12-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/162 |
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| author | S.Yu. Favorov |
| author_facet | S.Yu. Favorov |
| author_sort | S.Yu. Favorov |
| collection | DOAJ |
| description | We show that if points of supports of two discrete ”not very thick” Fourier transformable measures on locally compact abelian (LCA) groups tend to one another at infinity and the same is true for the masses at these points, then these measures coincide. The result is valid for discrete almost periodic measures on LCA groups too. Also, we show that the result is false for some discrete ”thick” measures. To do this, we construct a discrete almost periodic measure on the real axis, whose masses at the points of support tend to zero as these points approach infinity. |
| format | Article |
| id | doaj-art-475b9fce656e46cabc923845eef2c0a1 |
| institution | DOAJ |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2020-12-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-475b9fce656e46cabc923845eef2c0a12025-08-20T03:17:40ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202020-12-0154221121910.30970/ms.54.2.211-219162Uniqueness theorem for Fourier transformable measures on LCA groupsS.Yu. Favorov0Karazin National University of KharkivWe show that if points of supports of two discrete ”not very thick” Fourier transformable measures on locally compact abelian (LCA) groups tend to one another at infinity and the same is true for the masses at these points, then these measures coincide. The result is valid for discrete almost periodic measures on LCA groups too. Also, we show that the result is false for some discrete ”thick” measures. To do this, we construct a discrete almost periodic measure on the real axis, whose masses at the points of support tend to zero as these points approach infinity.http://matstud.org.ua/ojs/index.php/matstud/article/view/162fourier transformable measure; discrete support; almost periodic measure |
| spellingShingle | S.Yu. Favorov Uniqueness theorem for Fourier transformable measures on LCA groups Математичні Студії fourier transformable measure; discrete support; almost periodic measure |
| title | Uniqueness theorem for Fourier transformable measures on LCA groups |
| title_full | Uniqueness theorem for Fourier transformable measures on LCA groups |
| title_fullStr | Uniqueness theorem for Fourier transformable measures on LCA groups |
| title_full_unstemmed | Uniqueness theorem for Fourier transformable measures on LCA groups |
| title_short | Uniqueness theorem for Fourier transformable measures on LCA groups |
| title_sort | uniqueness theorem for fourier transformable measures on lca groups |
| topic | fourier transformable measure; discrete support; almost periodic measure |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/162 |
| work_keys_str_mv | AT syufavorov uniquenesstheoremforfouriertransformablemeasuresonlcagroups |