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This article is cited in 2 scientific papers (total in 2 papers)
Divergence of interpolation processes on sets of the second category
Al. A. Privalov
Abstract:
$C([0,1])$ is the space of real continuous functions $f(x)$ on $[0,1]$ and $\omega(\delta)$ is a majorant of the modulus of continuity $\omega(f,\delta)$, satisfying the condition $\varlimsup\limits_{n\to\infty}\omega(1/n)\ln n=\infty$. A solution is given to a problem of S. B. Stechkin: for any matrix $\mathfrak M$ of interpolation points there exists an $f(x)\in C([0,1])$, $\omega(f,\delta)=o\{\omega(\delta)\}$ whose Lagrange interpolation process diverges on a set $\mathscr E$ of second category on $[0,1]$.
Received: 21.06.1974
Citation:
Al. A. Privalov, “Divergence of interpolation processes on sets of the second category”, Mat. Zametki, 18:2 (1975), 179–183; Math. Notes, 18:2 (1975), 692–694
Linking options:
https://www.mathnet.ru/eng/mzm7640 https://www.mathnet.ru/eng/mzm/v18/i2/p179
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Abstract page: | 194 | Full-text PDF : | 82 | First page: | 1 |
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