This article is cited in 4 papers

Estimates for the widths of classes of periodic functions of several variables – I

D. B. Bazarkhanov

Institute of Mathematics, Almaty, Kazakhstan

Abstract: We establish estimates sharp in order for the Kolmogorov and linear widths of the classes $\mathrm{B}^{s\,m}_{p\,q}(\,\mathbb{T}^k)$ and $\mathrm{L}^{s\,m}_{p\,q}(\,\mathbb{T}^k)$ of Nikol'skii–Besov, Lizorkin–Triebel types respectively, in the space $L_r(\mathbb{T}^k)$ for a certain range of the parameters $s,p,q,r$, and $m$.

Keywords and phrases: Kolmogorov width, linear width, function class, mixed smoothness, wavelet.

MSC: 41A46, 41A63, 42C40

Received: 19.08.2010

Language: English

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