Abstract:
We obtain exact values of different $n$-widths for classes of differentiable periodic functions in the space $L_{2}[0,2\pi]$ satisfying the constraint
$$
\biggl(\int_{0}^{h}\omega_{m}^{p}(f^{(r)};t)\,dt\biggr)^{1/p}\le\Phi(h),
$$
where $0<h<\infty$, $1/r<p\le2$, $r\in\mathbb{N}$, and $\omega_{m}(f^{(r)};t)$ is the modulus of continuity of $m$th order of the derivative $f^{(r)}(x)\in L_{2}[0,2\pi]$.
Keywords:differentiable periodic function, width in the sense of Bernstein, Kolmogorov, Gelfand, the space $L_{2}[0,2\pi]$, trigonometric polynomial, Fourier series, modulus of continuity, linear operator.
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