This article is cited in 3 scientific papers (total in 3 papers)
Widths in $L_p$ of classes of continuous and of differentiable functions, and optimal methods of coding and recovering functions and their derivatives
N. P. Korneichuk
Exact values of linear widths (diameters), Kolmogorov widths and Gel'fand widths, in $L_p$-spaces are found for some classes of functions, using a convex majorant of the modulus of continuity of a function or its derivative. Precise constants in the Jackson type theorems on approximation of continuous and differentiable functions are also found. These results are interpreted from the point of view of problems of optimal coding and optimal recovery of functions and their derivatives.
Bibliography: 23 titles.
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Mathematics of the USSR-Izvestiya, 1982, 18:2, 227–247
MSC: Primary 41A65; Secondary 41A17, 41A50
N. P. Korneichuk, “Widths in $L_p$ of classes of continuous and of differentiable functions, and optimal methods of coding and recovering functions and their derivatives”, Izv. Akad. Nauk SSSR Ser. Mat., 45:2 (1981), 266–290; Math. USSR-Izv., 18:2 (1982), 227–247
Citation in format AMSBIB
\paper Widths in $L_p$ of classes of continuous and of differentiable functions, and optimal methods of coding and recovering functions and their derivatives
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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N. P. Korneichuk, “S. M. Nikol'skii and the development of research on approximation theory in the USSR”, Russian Math. Surveys, 40:5 (1985), 83–156
Erich Novak, “Quadrature and widths”, Journal of Approximation Theory, 47:3 (1986), 195
M. Sh. Shabozov, M. R. Langarshoev, “O nailuchshikh lineinykh metodakh priblizheniya nekotorykh klassov analiticheskikh v edinichnom kruge funktsii”, Sib. matem. zhurn., 60:6 (2019), 1414–1423
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