Abstract
Assume that 0<ε≤1, F ∈ C(\(\mathbb{T}\)), E={≠0}, δ>0. Then there exists a function G with uniformly convergent Fourier series such that |G|+|F−G|≤(1+δ)|F|, m{F≠G}≤εmE, and\(sup\left\{ {\left| {\sum\nolimits_{k \leqslant j \leqslant l} {\hat G(j)\zeta ^j } } \right|:\zeta \in \mathbb{T}, k \leqslant 1} \right\} \leqslant const\left\| F \right\|_\infty (1 + \log \varepsilon ^{ - 1} )\). Bibliography: 3 titles.
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Literature Cited
S. V. Kislyakov, “Quantitative aspect of correction theorems,”Zap. Nauchn. Semin. LOMI,92, 182–191 (1979).
S. A. Vinogradov, “A refinement of the Kolmogorov theorem on conjugate functions, and interpolation properties of uniformly convergent power series,”Tr. Mat. Inst. Akad. Nauk SSSR,130, 7–40 (1981).
S. V. Khrushchev and S. A. Vinogradov, “Free interpolation in the space of uniformly, convergent Taylor series,”Lect. Notes Math.,864, 171–213 (1981).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 217, 1994, pp. 83–91.
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Kislyakov, S.V. Quantitative aspect of correction theorems. II. J Math Sci 85, 1808–1813 (1997). https://doi.org/10.1007/BF02355291
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DOI: https://doi.org/10.1007/BF02355291