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)


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.


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