Geodesic
On the divergence of Lagrange interpolation processes on sets of the second category
Sbornik. Mathematics, Tome 55 (1986) no. 2, pp. 511-528 Cet article a éte moissonné depuis la source Math-Net.Ru

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If $\omega$ is a real nondecreasing semiadditive function, continuous on $[0;1]$, such that $\omega(0)=0$ and $\varlimsup_{n\to\infty}\omega\bigl(\frac1n\bigr)\ln n>0$, then for every matrix of interpolation knots on $[0;1]$ there are a function $f$, continuous on $[0;1]$, whose modulus of continuity $\omega(f,\delta)=O\{\omega(\delta)\}$, and a set $\mathscr E$ of second category on $[0;1]$ such that the Lagrange interpolation process for $f$ diverges everywhere on $\mathscr E$. Bibliography: 10 titles. 
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     author = {Al. A. Privalov},
     title = {On~the divergence of {Lagrange} interpolation processes on sets of the second category},
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     year = {1986},
     volume = {55},
     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/SM_1986_55_2_a12/}
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Al. A. Privalov. On the divergence of Lagrange interpolation processes on sets of the second category. Sbornik. Mathematics, Tome 55 (1986) no. 2, pp. 511-528. http://geodesic.mathdoc.fr/item/SM_1986_55_2_a12/

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