Exact values of the best mean approximations by algebraic polynomials of $$$W^r_L$$$ classes ($$$r=1,2$$$)

V.A. Kofanov

doi:10.15421/247705

Exact values of the best mean approximations by algebraic polynomials of $$$W^r_L$$$ classes ($$$r=1,2$$$)

V.A. Kofanov (Dnipropetrovsk State University), https://orcid.org/0000-0003-0392-2257

Abstract

In the paper, we have found the supremum of the best mean approximations by algebraic polynomials of differentiable functions from $$$W^r_L$$$ classes for $$$r=1,2$$$.

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References

Nikolskii S.M. "On the best linear method of mean approximation by polynomials of differentiable functions", DAN SSSR, 1947; 58(2): pp. 185-188. (in Russian)

Nikolskii S.M. "Mean approximation of functions by trigonometrical polynomials", Izv. AN SSSR. Ser.: Matematika, 1946; 10(3): pp. 207-256. (in Russian)

DOI: https://doi.org/10.15421/247705