A uniqueness theorem for meromorphic functions
In this paper, we prove the uniqueness theorem for a special class of meromorphic functions on the complex plane $\mathbb{C}$. In particular, we study the class of meromorphic functions $f$ in the domain $\mathbb{C}\setminus K'$, where $K'$ is the finite set of limit points of simple poles...
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| Format: | Article |
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Ivan Franko National University of Lviv
2024-06-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/510 |
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| author | N. Sushchyk D. Lukivska |
| author_facet | N. Sushchyk D. Lukivska |
| author_sort | N. Sushchyk |
| collection | DOAJ |
| description | In this paper, we prove the uniqueness theorem for a special class of meromorphic functions on the complex plane $\mathbb{C}$. In particular, we study the class of meromorphic functions $f$ in the domain $\mathbb{C}\setminus K'$, where $K'$ is the finite set of limit points of simple poles of the function $f$. In this class, we describe non-trivial subclasses in which every function $f$ can be uniquely determined by the residues of the function $f$ at its poles. The result covered in this paper is a part of a problem in a spectral operator theory. |
| format | Article |
| id | doaj-art-38e2798a656541aa8003d841ea051651 |
| institution | Kabale University |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2024-06-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-38e2798a656541aa8003d841ea0516512025-08-20T03:33:27ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202024-06-0161221922410.30970/ms.61.2.219-224510A uniqueness theorem for meromorphic functionsN. Sushchyk0D. Lukivska1Ivan Franko National University of LvivIvan Franko National University of LvivIn this paper, we prove the uniqueness theorem for a special class of meromorphic functions on the complex plane $\mathbb{C}$. In particular, we study the class of meromorphic functions $f$ in the domain $\mathbb{C}\setminus K'$, where $K'$ is the finite set of limit points of simple poles of the function $f$. In this class, we describe non-trivial subclasses in which every function $f$ can be uniquely determined by the residues of the function $f$ at its poles. The result covered in this paper is a part of a problem in a spectral operator theory.http://matstud.org.ua/ojs/index.php/matstud/article/view/510meromorphic functionsblaschke products |
| spellingShingle | N. Sushchyk D. Lukivska A uniqueness theorem for meromorphic functions Математичні Студії meromorphic functions blaschke products |
| title | A uniqueness theorem for meromorphic functions |
| title_full | A uniqueness theorem for meromorphic functions |
| title_fullStr | A uniqueness theorem for meromorphic functions |
| title_full_unstemmed | A uniqueness theorem for meromorphic functions |
| title_short | A uniqueness theorem for meromorphic functions |
| title_sort | uniqueness theorem for meromorphic functions |
| topic | meromorphic functions blaschke products |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/510 |
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