Мақаланы E-mail арқылы жіберу On $C^m$-reflection of harmonic functions and $C^m$-approximation by harmonic polynomials
- Авторлар: Paramonov P.V.1,2, Fedorovskiy K.Y.2,3
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Мекемелер:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Bauman Moscow State Technical University
- Saint Petersburg State University
- Шығарылым: Том 211, № 8 (2020)
- Беттер: 102-113
- Бөлім: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/133342
- DOI: https://doi.org/10.4213/sm9295
- ID: 133342
Дәйексөз келтіру
Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Аннотация
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.
Авторлар туралы
Petr Paramonov
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics; Bauman Moscow State Technical University
Email: petr.paramonov@list.ru
Konstantin Fedorovskiy
Bauman Moscow State Technical University; Saint Petersburg State University
Email: kfedorovs@yandex.ru
Doctor of physico-mathematical sciences, Associate professor
Әдебиет тізімі
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- K. Fedorovskiy, P. Paramonov, “On $operatorname{Lip}^m$-reflection of harmonic functions over boundaries of simple Caratheodory domains”, Anal. Math. Phys., 9:3 (2019), 1031–1042
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