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- W2950559612 abstract "Estimates of Kolmogorov $n$-widths $d_n(B_p^r, L^q)$ and linear $n$-widths $da_n(B_p^r, L^q)$, ($1leq qleq infty$) of Sobolev's classes $B_p^r$, ($r>0$, $1leq pleq infty$) on compact two-point homogeneous spaces (CTPHS) are established. For part of $(p, q)in[1,infty]times[1,infty]$, sharp orders of $d_n(B_p^r, L^q)$ or $da_n (B_p^r, L^q) $ were obtained by Bordin, Kushpel, Levesley and Tozoni in a recent paper `` J. Funct. Anal. 202 (2) (2003), 307--326''. In this paper, we obtain the sharp orders of $d_n(B_p^r, L^q)$ and $da_n (B_p^r, L^q)$ for all the remaining $ (p,q)$. Our proof is based on positive cubature formulas and Marcinkiewicz-Zygmund type inequalities on CTPHS." @default.
- W2950559612 created "2019-06-27" @default.
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- W2950559612 date "2005-09-30" @default.
- W2950559612 modified "2023-09-25" @default.
- W2950559612 title "Approximation of smooth functions on compact two-point homogeneous spaces" @default.
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