Extremal decomposition of a multidimensional complex space for five domains
- Авторлар: Zabolotnii Y.1, Denega I.1
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Мекемелер:
- Institute of Mathematics of the National Academy of Sciences of Ukraine
- Шығарылым: Том 241, № 1 (2019)
- Беттер: 101-108
- Бөлім: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242863
- DOI: https://doi.org/10.1007/s10958-019-04410-x
- ID: 242863
Дәйексөз келтіру
Аннотация
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.
Авторлар туралы
Yaroslav Zabolotnii
Institute of Mathematics of the National Academy of Sciences of Ukraine
Хат алмасуға жауапты Автор.
Email: yaroslavzabolotnii@gmail.com
Украина, Kyiv
Iryna Denega
Institute of Mathematics of the National Academy of Sciences of Ukraine
Email: yaroslavzabolotnii@gmail.com
Украина, Kyiv