Extremal decomposition of multidimensional complex space for five domains
The paper is devoted to one open extremal problem in the geometric function theory of complex variables associated with estimates of a functional defined on the systems of non-overlapping domains. We consider the problem of the maximum of a product of inner radii of n non-overlapping domains contain...
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| Опубліковано в: : | Український математичний вісник |
|---|---|
| Дата: | 2018 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2018
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/169414 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Extremal decomposition of multidimensional complex space for five domains / Y. Zabolotnii, I. Denega // Український математичний вісник. — 2018. — Т. 15, № 3. — С. 431-441. — Бібліогр.: 21 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862566251650351104 |
|---|---|
| author | Zabolotni, i Y. Denega, I. |
| author_facet | Zabolotni, i Y. Denega, I. |
| citation_txt | Extremal decomposition of multidimensional complex space for five domains / Y. Zabolotnii, I. Denega // Український математичний вісник. — 2018. — Т. 15, № 3. — С. 431-441. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Український математичний вісник |
| description | The paper is devoted to one open extremal problem in the geometric function theory of complex variables associated with estimates of a functional defined on the systems of non-overlapping domains. We consider the problem of the maximum of a product of inner radii of n non-overlapping domains containing points of a unit circle and the power γ of the inner radius of a domain containing the origin. The problem was formulated in 1994 in Dubinin’s paper in the journal “Russian Mathematical Surveys” in the list of unsolved problems and then repeated in his monograph in 2014. Currently, it is not solved in general. In this paper, we obtained a solution of the problem for five simply connected domains and power γ ∈ (1, 2.57] and generalized this result to the case of multidimensional complex space.
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| first_indexed | 2025-11-26T00:08:44Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-169414 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1810-3200 |
| language | English |
| last_indexed | 2025-11-26T00:08:44Z |
| publishDate | 2018 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Zabolotni, i Y. Denega, I. 2020-06-12T17:53:31Z 2020-06-12T17:53:31Z 2018 Extremal decomposition of multidimensional complex space for five domains / Y. Zabolotnii, I. Denega // Український математичний вісник. — 2018. — Т. 15, № 3. — С. 431-441. — Бібліогр.: 21 назв. — англ. 1810-3200 010 MSC. 30C75, 32A30 https://nasplib.isofts.kiev.ua/handle/123456789/169414 The paper is devoted to one open extremal problem in the geometric function theory of complex variables associated with estimates of a functional defined on the systems of non-overlapping domains. We consider the problem of the maximum of a product of inner radii of n non-overlapping domains containing points of a unit circle and the power γ of the inner radius of a domain containing the origin. The problem was formulated in 1994 in Dubinin’s paper in the journal “Russian Mathematical Surveys” in the list of unsolved problems and then repeated in his monograph in 2014. Currently, it is not solved in general. In this paper, we obtained a solution of the problem for five simply connected domains and power γ ∈ (1, 2.57] and generalized this result to the case of multidimensional complex space. en Інститут прикладної математики і механіки НАН України Український математичний вісник Extremal decomposition of multidimensional complex space for five domains Article published earlier |
| spellingShingle | Extremal decomposition of multidimensional complex space for five domains Zabolotni, i Y. Denega, I. |
| title | Extremal decomposition of multidimensional complex space for five domains |
| title_full | Extremal decomposition of multidimensional complex space for five domains |
| title_fullStr | Extremal decomposition of multidimensional complex space for five domains |
| title_full_unstemmed | Extremal decomposition of multidimensional complex space for five domains |
| title_short | Extremal decomposition of multidimensional complex space for five domains |
| title_sort | extremal decomposition of multidimensional complex space for five domains |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/169414 |
| work_keys_str_mv | AT zabolotniiy extremaldecompositionofmultidimensionalcomplexspaceforfivedomains AT denegai extremaldecompositionofmultidimensionalcomplexspaceforfivedomains |