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

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