Classes of functions in the set of circulant matrices and their characterization
UDC 512.5 We introduce new classes of functions generalizing the well-known classes of functions of complex variable, such as the entire functions, meromorphic functions, rational functions, and polynomial functions, which take values in the set of circulant matrices with complex entries. For these...
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| Date: | 2026 |
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| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9230 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513452673466368 |
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| author | Abramov, Vyacheslav M. Abramov, Vyacheslav M. |
| author_facet | Abramov, Vyacheslav M. Abramov, Vyacheslav M. |
| author_sort | Abramov, Vyacheslav M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
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| datestamp_date | 2026-03-21T13:35:21Z |
| description | UDC 512.5
We introduce new classes of functions generalizing the well-known classes of functions of complex variable, such as the entire functions, meromorphic functions, rational functions, and polynomial functions, which take values in the set of circulant matrices with complex entries. For these new classes of functions, we extend some recently obtained characterization theorems presented in [B. Q. Li, Amer. Math. Monthly, 122, № 2, 169–172 (2015)] and [B. Q. Li, Amer. Math. Monthly, 132, № 3, 269–271 (2025)] to an algebraic structure of circulant matrices that includes several complex variables. Our characterization theorems generalize a recently established version of the fundamental theorem of algebra presented in [V. M. Abramov, Amer. Math. Monthly, 132, № 4, 356–360 (2025)]. |
| doi_str_mv | 10.3842/umzh.v77i11.9230 |
| first_indexed | 2026-03-24T03:44:55Z |
| format | Article |
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| id | umjimathkievua-article-9230 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:44:55Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-92302026-03-21T13:35:21Z Classes of functions in the set of circulant matrices and their characterization Classes of functions in the set of circulant matrices and their characterization Abramov, Vyacheslav M. Abramov, Vyacheslav M. Functions of complex variable entire functions meromorphic functions rational functions circulant matrices matrix equations fundamental theorem of algebra Functions of complex variable circulant matrices matrix equations fundamental theorem of algebra entire functions meromorphic functions rational functions UDC 512.5 We introduce new classes of functions generalizing the well-known classes of functions of complex variable, such as the entire functions, meromorphic functions, rational functions, and polynomial functions, which take values in the set of circulant matrices with complex entries. For these new classes of functions, we extend some recently obtained characterization theorems presented in [B. Q. Li, Amer. Math. Monthly, 122, № 2, 169–172 (2015)] and [B. Q. Li, Amer. Math. Monthly, 132, № 3, 269–271 (2025)] to an algebraic structure of circulant matrices that includes several complex variables. Our characterization theorems generalize a recently established version of the fundamental theorem of algebra presented in [V. M. Abramov, Amer. Math. Monthly, 132, № 4, 356–360 (2025)]. УДК 512.5 Класи функцій у множині циркулянтних матриць та їхня характеристика Уведено нові класи функцій, що узагальнюють відомі класи функцій комплексної змінної, зокрема цілі, мероморфні, раціональні та поліноміальні функції, і набувають значень на множині циркулянтних матриць із комплексними елементами. Для цих нових класів функцій поширено нещодавно отримані теореми характеристик, що наведені в [B. Q. Li, Amer. Math. Monthly, 122, № 2, 169–172 (2015)] і [B. Q. Li, Amer. Math. Monthly, 132, № 3, 269–271 (2025)], на алгебраїчну структуру циркулянтних матриць для випадку кількох комплексних змінних. Отримані теореми характеристик %привели до узагальнюють варіант основної теореми алгебри, що був нещодавно наведений в [V. M. Abramov, Amer. Math. Monthly, 132, № 4, 356–360 (2025)]. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9230 10.3842/umzh.v77i11.9230 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 11 (2025); 692–693 Український математичний журнал; Том 77 № 11 (2025); 692–693 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9230/10599 Copyright (c) 2025 Vyacheslav M. Abramov |
| spellingShingle | Abramov, Vyacheslav M. Abramov, Vyacheslav M. Classes of functions in the set of circulant matrices and their characterization |
| title | Classes of functions in the set of circulant matrices and their characterization |
| title_alt | Classes of functions in the set of circulant matrices and their characterization |
| title_full | Classes of functions in the set of circulant matrices and their characterization |
| title_fullStr | Classes of functions in the set of circulant matrices and their characterization |
| title_full_unstemmed | Classes of functions in the set of circulant matrices and their characterization |
| title_short | Classes of functions in the set of circulant matrices and their characterization |
| title_sort | classes of functions in the set of circulant matrices and their characterization |
| topic_facet | Functions of complex variable entire functions meromorphic functions rational functions circulant matrices matrix equations fundamental theorem of algebra Functions of complex variable circulant matrices matrix equations fundamental theorem of algebra entire functions meromorphic functions rational functions |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9230 |
| work_keys_str_mv | AT abramovvyacheslavm classesoffunctionsinthesetofcirculantmatricesandtheircharacterization AT abramovvyacheslavm classesoffunctionsinthesetofcirculantmatricesandtheircharacterization |