On widths of one class of periodic functions

V.G. Doronin; A.A. Ligun

doi:10.15421/247704

On widths of one class of periodic functions

V.G. Doronin (Dnipropetrovsk State University)
A.A. Ligun (Dnipropetrovsk State University)

Abstract

In the paper, we have found the A.N. Kolmogorov's width of the class $$$W^r L^+_p$$$ ($$$r=1,2,\ldots$$$, $$$1 \leqslant p \leqslant \infty$$$) of all $$$2\pi$$$-periodic functions $$$f(x)$$$ whose $$$(r-1)$$$-th derivative $$$f^{(r-1)}(x)$$$ is absolutely continuous and $$$\| f^{(r)}_+ \|_p \leqslant 1$$$.

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References

Motornyi V.P., Ruban V.I. "Widths of some classes of differentiable periodic functions in $$$L$$$ space", Math. Notes, 1975; 17(4): pp. 531-543. doi:10.1007/BF01105381

Stein E.M. "Functions of exponential type", Ann. Math., 1957; 65(3): pp. 582-592. doi:10.2307/1970066

Kolmogorov A.N. "On inequalities between upper bounds of consecutive derivatives of the function on infinite interval", Uch. zap. MGU. Matem., 1939; 30(3): pp. 3-16.

Doronin V.G., Ligun A.A. "Exact values of upper bounds of the best approximations of $$$W^r_+ L_{\Phi}$$$ classes in $$$L$$$ metric", Res. Math., 1976; pp. 25-34.

Korneichuk N.P. Extremum problems in approximation theory, 1976.