Email this article On the density of the additive semigroup generated by a subset of a Hilbert–Schmidt ellipsoid
- Authors: Shklyaev K.S.1,2
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Affiliations:
- Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
- Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
- Issue: Vol 216, No 6 (2025)
- Pages: 138-150
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/306717
- DOI: https://doi.org/10.4213/sm10132
- ID: 306717
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Abstract
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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About the authors
Konstantin Sergeevich 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
References
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