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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| Дата: | 2026 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2026
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/9230 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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)]. |
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| DOI: | 10.3842/umzh.v77i11.9230 |