Random variables determined by the distributions of their digits in a numeration system with complex base
We study the distributions of complex-valued random variables determined by the distributions of their digits in a numeration system with complex base. We establish sufficient conditions for the singularity of such random variables, in particular, in the cases where their spectrum has Lebesgue measu...
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| Datum: | 1998 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1998
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4793 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510964812611584 |
|---|---|
| author | O., V. Shkol’nyi Школьний, О. В. |
| author_facet | O., V. Shkol’nyi Школьний, О. В. |
| author_sort | O., V. Shkol’nyi |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:14:27Z |
| description | We study the distributions of complex-valued random variables determined by the distributions of their digits in a numeration system with complex base. We establish sufficient conditions for the singularity of such random variables, in particular, in the cases where their spectrum has Lebesgue measure zero (C-type singular distribution) or is a rectangle (S-type singular distribution). |
| first_indexed | 2026-03-24T03:05:22Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4793 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:05:22Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/8f/1f174cb413162930077bf6827e5aae8f.pdf |
| spelling | umjimathkievua-article-47932020-03-18T21:14:27Z Random variables determined by the distributions of their digits in a numeration system with complex base Випадкові величини, задані розподілами своїх цифр у системі числення з комплексною основою O., V. Shkol’nyi Школьний, О. В. We study the distributions of complex-valued random variables determined by the distributions of their digits in a numeration system with complex base. We establish sufficient conditions for the singularity of such random variables, in particular, in the cases where their spectrum has Lebesgue measure zero (C-type singular distribution) or is a rectangle (S-type singular distribution). Вивчаються розподіли комплекснозиачних випадкових величин, заданих розподілами своїх цифр у системі числення з комплексною основою. Знайдено достатні умови сингулярності таких випадкових величии, зокрема, коли їх спектр має нульову міру Лебега (сингулярний розподіл $C$-типу) чи є прямокутником (сингулярний розподіл 5-типу). Institute of Mathematics, NAS of Ukraine 1998-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4793 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 12 (1998); 1715–1720 Український математичний журнал; Том 50 № 12 (1998); 1715–1720 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4793/6286 https://umj.imath.kiev.ua/index.php/umj/article/view/4793/6287 Copyright (c) 1998 O. V. Shkol’nyi |
| spellingShingle | O., V. Shkol’nyi Школьний, О. В. Random variables determined by the distributions of their digits in a numeration system with complex base |
| title | Random variables determined by the distributions of their digits in a numeration system with complex base |
| title_alt | Випадкові величини, задані розподілами своїх цифр у системі числення
з комплексною основою |
| title_full | Random variables determined by the distributions of their digits in a numeration system with complex base |
| title_fullStr | Random variables determined by the distributions of their digits in a numeration system with complex base |
| title_full_unstemmed | Random variables determined by the distributions of their digits in a numeration system with complex base |
| title_short | Random variables determined by the distributions of their digits in a numeration system with complex base |
| title_sort | random variables determined by the distributions of their digits in a numeration system with complex base |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4793 |
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