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Zapiski Nauchnykh Seminarov POMI, 1994, Volume 217, Pages 83–91 (Mi znsl5962)  

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
Full-text PDF (416 kB) Citations (2)
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
English version:
Journal of Mathematical Sciences (New York), 1997, Volume 85, Issue 2, Pages 1808–1813
DOI: https://doi.org/10.1007/BF02355291
Bibliographic databases:
Document Type: Article
UDC: 517.513
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Kis94}
\by S.~V.~Kislyakov
\paper Quantitative aspect of correction theorems.~II
\inbook Investigations on linear operators and function theory. Part~22
\serial Zap. Nauchn. Sem. POMI
\yr 1994
\vol 217
\pages 83--91
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5962}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1327517}
\zmath{https://zbmath.org/?q=an:0867.42006|0907.42007}
\transl
\jour J. Math. Sci. (New York)
\yr 1997
\vol 85
\issue 2
\pages 1808--1813
\crossref{https://doi.org/10.1007/BF02355291}
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  • https://www.mathnet.ru/eng/znsl/v217/p83
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