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Quantitative aspect of correction theorems. II

Authors:	S V Kislyakov

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. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 217, 1994, pp. 83–91.

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