Email this article On $C^m$-reflection of harmonic functions and $C^m$-approximation by harmonic polynomials
- Authors: Paramonov P.V.1,2, Fedorovskiy K.Y.2,3
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Affiliations:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Bauman Moscow State Technical University
- Saint Petersburg State University
- Issue: Vol 211, No 8 (2020)
- Pages: 102-113
- Section: Articles
- URL: https://bakhtiniada.ru/0368-8666/article/view/133342
- DOI: https://doi.org/10.4213/sm9295
- ID: 133342
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Abstract
We obtain several new sharp $C^m$-continuity conditions, both necessary and sufficient, for operators of harmonic reflection of functions over boundaries of simple Caratheodory domains in $\mathbb R^N$. These results are based on a new criterion (also obtained in this paper) for $C^m$-continuity of the Poisson operator in the aforesaid domains. As corollaries, we give new sufficient conditions for $C^m$-approximability of functions by harmonic polynomials on boundaries of simple Caratheodory domains in $\mathbb R^N$. Bibliography: 17 titles.
About the authors
Petr Vladimirovich Paramonov
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics; Bauman Moscow State Technical University
Email: petr.paramonov@list.ru
Konstantin Yurievich Fedorovskiy
Bauman Moscow State Technical University; Saint Petersburg State University
Email: kfedorovs@yandex.ru
Doctor of physico-mathematical sciences, Associate professor
References
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