Мақаланы E-mail арқылы жіберу On the density of the additive semigroup generated by a subset of a Hilbert–Schmidt ellipsoid
- Авторлар: Shklyaev K.S.1,2
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Мекемелер:
- Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
- Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
- Шығарылым: Том 216, № 6 (2025)
- Беттер: 138-150
- Бөлім: Articles
- URL: https://ogarev-online.ru/0368-8666/article/view/306717
- DOI: https://doi.org/10.4213/sm10132
- ID: 306717
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Аннотация
We obtain a criterion for the density of the additive semigroup generated by a subset of an ellipsoid in a Hilbert space with finite sum of the squared semiaxes. This criterion is then applied to the semigroups generated by the images of sets under holomorphic maps. As a consequence, we obtain a result on the uniform approximation of a holomorphic function on compact subsets by sums of shifts of a single function, which generalizes Korevaar's theorem.
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Авторлар туралы
Konstantin Shklyaev
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia; Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
Email: konstantin.shklyaev@inbox.ru
without scientific degree, no status
Әдебиет тізімі
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- W. Banaszczyk, “A Beck–Fiala-type theorem for Euclidean norms”, European J. Combin., 11:6 (1990), 497–500
- В. Н. Судаков, “Об одном классе компактов гильбертова пространства”, УМН, 18:1(109) (1963), 181–187
- A. Cohen, R. DeVore, “Kolmogorov widths under holomorphic mappings”, IMA J. Numer. Anal., 36:1 (2016), 1–12
- J. Korevaar, “Asymptotically neutral distributions of electrons and polynomial approximation”, Ann. of Math. (2), 80:3 (1964), 403–410
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