Extremal subspaces in the problem about widths of $$$H_{\omega}$$$ classes in the space of continuous functions of two variables

L.B. Khodak (Dnipropetrovsk State University)

Abstract


In the paper, we have pointed out the conditions under which the subspaces of dimensionality $$$n^2$$$ ($$$n=2,3,\ldots$$$), extremal for $$$H_{\omega}$$$ classes of continuous functions of two variables, do not exist.

References


Tikhomirov V.M. "Set widths in functional spaces and theory of the best approximations", Uspekhi mat. nauk, 1960; 15(3): pp. 81-120. (in Russian) doi:10.1070/RM1960v015n03ABEH004093

Ruban V.I. "Extremal subspaces in the problem about widths of $$$H_{\omega}[a, b]$$$ classes in $$$C_{[a, b]}$$$ space", Anal. Mat., 1975; 1: pp. 131-139. (in Russian)

Tikhomirov V.M. Some problems of approximation theory, Izd-vo Moskovskogo un-ta, 1976. (in Russian)

Lorentz G.G. Approximation of functions, Holt, Rinehart and Winston, 1966.




DOI: https://doi.org/10.15421/247709

  

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Copyright (c) 1977 L.B. Khodak

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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