Corrections to the article On the Theory of Interpolation (DAN, vol. 163, no. 3, 1965)
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PHYSICS
L. A. Vasiliev, I. V. Ershov, E. V. Sokolenko, V. I. Ianichkin. Interferometer with diffraction grating used for studying the flow past models in a shock tube . . . 1245
B. M. Moiseev, L. I. Fedorov. Complex splitting of nuclear magnetic resonance spectrum of a two-spin system . . . 1249
K. P. Staniukovich. Radiation by elementary particles . . . 1252
G. V. Sholin. Anomalous energy dependence of the polarisation of the radiation of atoms excited by an electron beam . . . 1256
TECHNICAL PHYSICS
A. I. Beliaev, A. I. Iukova. The influence of the third component on the behaviour of impurities in zone-melting of aluminium . . . 1259
Iu. A. Skakov. The nature of disintegration products and the liberation mechanism in the ageing of tempered commercial iron . . . 1263
N. E. Filonenko, V. I. Ivanov, L. I. Feldgun, M. I. Sokhor, L. F. Vereshchagin. Magnesium borides produced under superhigh pressure . . . 1266
V. V. Shevelia, B. I. Kostetskii. The influence of surface-active media on the formation of dislocation structure in the case of fatigue of metals . . . 1270
GEOPHYSICS
E. N. Mikhailova, A. I. Felsenbaum, N. B. Shapiro. On the calculation of ice-field drifts and currents in the Arctic basin . . . 1273
CRYSTALLOGRAPHY
L. D. Kislovskii. Metastable structures in aqueous solutions . . . 1277
ERRATUM
In my article (D. L. Berman, “On the Theory of Interpolation”), published in DAN, vol. 163, no. 3, 1965, the following corrections must be made.
Theorem 1 should be formulated as follows:
The Lagrange interpolation process, constructed for functions from the Dini–Lipschitz class at the nodes (2), converges uniformly on \([-1, 1]\).
Inequality (4) on p. 552 is incorrect.
In Theorem 3, the equality \(\lim_{n\to\infty} H_n(f, 0)=\infty\) should be replaced by the inequality
\[ \overline{\lim}_{n\to\infty} H_n(f,0) > \frac{1}{2}. \]
Equality (6) on p. 553 should have the form
\[ \sum_{j=1}^{2n} \frac{1}{\sin^4 \varphi_j/2} = \frac{16}{3}n^4 + \frac{8}{3}n^2 . \]
D. L. Berman
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