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Zapiski Nauchnykh Seminarov POMI, 1994, Volume 217, Pages 83–91
(Mi znsl5962)
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This article is cited in 2 scientific papers (total in 2 papers)
Quantitative aspect of correction theorems. II
S. V. Kislyakov St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences
Abstract:
Let $0<\varepsilon\le1$, $F\in C(\mathbb T)$, $E=\{F\ne0\}$, $\delta>0$. Then there exists a function $G$ with uniformly convergent Fourier series such that $|G|+|F-G|\le(1+\delta)|F|$, $m\{F\ne G\}\le\varepsilon mE$ and $\sup\{|\sum_{k\le j\le l}\hat G(j)\zeta^j|\colon\zeta\in\mathbb T,\ k\le l\}\le\mathrm{const}\|F\|_\infty(1+\log\varepsilon^{-1})$. Bibliography: 3 titles.
Received: 20.12.1993
Citation:
S. V. Kislyakov, “Quantitative aspect of correction theorems. II”, Investigations on linear operators and function theory. Part 22, Zap. Nauchn. Sem. POMI, 217, POMI, St. Petersburg, 1994, 83–91; J. Math. Sci. (New York), 85:2 (1997), 1808–1813
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https://www.mathnet.ru/eng/znsl5962 https://www.mathnet.ru/eng/znsl/v217/p83
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